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Título : Fourier Integral Operators Tipo de documento: documento electrónico Autores: J.J. Duistermaat ; SpringerLink (Online service) Editorial: Boston : Birkhäuser Boston Fecha de publicación: 2011 Colección: Modern Birkhäuser Classics Número de páginas: IX, 142 p Il.: online resource ISBN/ISSN/DL: 978-0-8176-8108-1 Idioma : Inglés (eng) Palabras clave: Mathematics Fourier analysis Integral equations Operator theory Partial differential Analysis Equations Theory Differential Clasificación: 51 Matemáticas Resumen: This volume is a useful introduction to the subject of Fourier integral operators and is based on the author's classic set of notes. Covering a range of topics from Hörmander’s exposition of the theory, Duistermaat approaches the subject from symplectic geometry and includes applications to hyperbolic equations (= equations of wave type) and oscillatory asymptotic solutions which may have caustics. This text is suitable for mathematicians and (theoretical) physicists with an interest in (linear) partial differential equations, especially in wave propagation, resp. WKB-methods. Familiarity with analysis (distributions and Fourier transformation) and differential geometry is useful. Additionally, this book is designed for a one-semester introductory course on Fourier integral operators aimed at a broad audience. This book remains a superb introduction to the theory of Fourier integral operators. While there are further advances discussed in other sources, this book can still be recommended as perhaps the very best place to start in the study of this subject. —SIAM Review This book is still interesting, giving a quick and elegant introduction to the field, more adapted to nonspecialists. —Zentralblatt MATH The book is completed with applications to the Cauchy problem for strictly hyperbolic equations and caustics in oscillatory integrals. The reader should have some background knowledge in analysis (distributions and Fourier transformations) and differential geometry. —Acta Sci. Math Nota de contenido: Preface -- 0. Introduction -- 1. Preliminaries -- 1.1 Distribution densities on manifolds -- 1.2 The method of stationary phase -- 1.3 The wave front set of a distribution -- 2. Local Theory of Fourier Integrals -- 2.1 Symbols -- 2.2 Distributions defined by oscillatory integrals -- 2.3 Oscillatory integrals with nondegenerate phase functions -- 2.4 Fourier integral operators (local theory) -- 2.5 Pseudodifferential operators in Rn -- 3. Symplectic Differential Geometry -- 3.1 Vector fields -- 3.2 Differential forms -- 3.3 The canonical 1- and 2-form T* (X) -- 3.4 Symplectic vector spaces -- 3.5 Symplectic differential geometry -- 3.6 Lagrangian manifolds -- 3.7 Conic Lagrangian manifolds -- 3.8 Classical mechanics and variational calculus -- 4. Global Theory of Fourier Integral Operators -- 4.1 Invariant definition of the principal symbol -- 4.2 Global theory of Fourier integral operators -- 4.3 Products with vanishing principal symbol -- 4.4 L2-continuity -- 5. Applications -- 5.1 The Cauchy problem for strictly hyperbolic differential operators with C-infinity coefficients -- 5.2 Oscillatory asymptotic solutions. Caustics -- References En línea: http://dx.doi.org/10.1007/978-0-8176-8108-1 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33103 Fourier Integral Operators [documento electrónico] / J.J. Duistermaat ; SpringerLink (Online service) . - Boston : Birkhäuser Boston, 2011 . - IX, 142 p : online resource. - (Modern Birkhäuser Classics) .
ISBN : 978-0-8176-8108-1
Idioma : Inglés (eng)
Palabras clave: Mathematics Fourier analysis Integral equations Operator theory Partial differential Analysis Equations Theory Differential Clasificación: 51 Matemáticas Resumen: This volume is a useful introduction to the subject of Fourier integral operators and is based on the author's classic set of notes. Covering a range of topics from Hörmander’s exposition of the theory, Duistermaat approaches the subject from symplectic geometry and includes applications to hyperbolic equations (= equations of wave type) and oscillatory asymptotic solutions which may have caustics. This text is suitable for mathematicians and (theoretical) physicists with an interest in (linear) partial differential equations, especially in wave propagation, resp. WKB-methods. Familiarity with analysis (distributions and Fourier transformation) and differential geometry is useful. Additionally, this book is designed for a one-semester introductory course on Fourier integral operators aimed at a broad audience. This book remains a superb introduction to the theory of Fourier integral operators. While there are further advances discussed in other sources, this book can still be recommended as perhaps the very best place to start in the study of this subject. —SIAM Review This book is still interesting, giving a quick and elegant introduction to the field, more adapted to nonspecialists. —Zentralblatt MATH The book is completed with applications to the Cauchy problem for strictly hyperbolic equations and caustics in oscillatory integrals. The reader should have some background knowledge in analysis (distributions and Fourier transformations) and differential geometry. —Acta Sci. Math Nota de contenido: Preface -- 0. Introduction -- 1. Preliminaries -- 1.1 Distribution densities on manifolds -- 1.2 The method of stationary phase -- 1.3 The wave front set of a distribution -- 2. Local Theory of Fourier Integrals -- 2.1 Symbols -- 2.2 Distributions defined by oscillatory integrals -- 2.3 Oscillatory integrals with nondegenerate phase functions -- 2.4 Fourier integral operators (local theory) -- 2.5 Pseudodifferential operators in Rn -- 3. Symplectic Differential Geometry -- 3.1 Vector fields -- 3.2 Differential forms -- 3.3 The canonical 1- and 2-form T* (X) -- 3.4 Symplectic vector spaces -- 3.5 Symplectic differential geometry -- 3.6 Lagrangian manifolds -- 3.7 Conic Lagrangian manifolds -- 3.8 Classical mechanics and variational calculus -- 4. Global Theory of Fourier Integral Operators -- 4.1 Invariant definition of the principal symbol -- 4.2 Global theory of Fourier integral operators -- 4.3 Products with vanishing principal symbol -- 4.4 L2-continuity -- 5. Applications -- 5.1 The Cauchy problem for strictly hyperbolic differential operators with C-infinity coefficients -- 5.2 Oscillatory asymptotic solutions. Caustics -- References En línea: http://dx.doi.org/10.1007/978-0-8176-8108-1 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33103 Ejemplares
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Título : A Friendly Guide to Wavelets Tipo de documento: documento electrónico Autores: Gerald Kaiser ; SpringerLink (Online service) Editorial: Boston : Birkhäuser Boston Fecha de publicación: 2011 Colección: Modern Birkhäuser Classics Número de páginas: XX, 300 p. 33 illus Il.: online resource ISBN/ISSN/DL: 978-0-8176-8111-1 Idioma : Inglés (eng) Palabras clave: Mathematics Fourier analysis Applied mathematics Engineering Physics Applications of Signal, Image and Speech Processing Mathematical Methods in Analysis Clasificación: 51 Matemáticas Resumen: I wholeheartedly recommend this book for a solid and friendly introduction to wavelets, for anyone who is comfortable with the mathematics required of undergraduate electrical engineers. The book's appeal is that it covers all the fundamental concepts of wavelets in an elegant, straightforward way. It offers truly enjoyable (friendly!) mathematical exposition that is rich in intuitive explanations, as well as clean, direct, and clear in its theoretical developments. I found Kaiser's straightforward end-of-chapter exercises excellent...Kaiser has written an excellent introduction to the fundamental concepts of wavelets. For a book of its length and purpose, I think it should be essentially unbeatable for a long time. —Proceedings of the IEEE It is well produced and certainly readable...This material should present no difficulty for fourth-year undergraduates...It also will be useful to advanced workers in that it presents a different approach to wavelet theory from the usual one. —Computing Reviews I found this to be an excellent book. It is eminently more readable than the books...which might be considered the principal alternatives for textbooks on wavelets. —Physics Today This volume is probably the most gentle introduction to wavelet theory on the market. As such, it responds to a significant need. The intended audience will profit from the motivation and common-sense explanations in the text. Ultimately, it may lead many readers, who may not otherwise have been able to do so, to go further into wavelet theory, Fourier analysis, and signal processing. —SIAM Review The first half of the book is appropriately named. It is a well-written, nicely organized exposition...a welcome addition to the literature. The second part of the book introduces the concept of electromagnetic wavelets...This theory promises to have many other applications and could well lead to new ways of studying these topics. This book has a number of unique features which...makes it particularly valuable for newcomers to the field. —Mathematical Reviews The book is indeed what its title promises: A friendly guide to wavelets...In short, Kaiser's book is excellently written and can be considered as one of the best textbooks on this topic presently available...it will enjoy wide distribution among mathematicians and physicists interested in wavelet analysis. —Internationale Mathematische Nachrichten For additional review samples and related material, please visit the author's website at www.wavelets.com Nota de contenido: Preface -- Suggestions to the Reader -- Symbols, Conventions, and Transforms -- Part I: Basic Wavelet Analysis. Preliminaries: Background and Notation -- Windowed Fourier Transforms -- Continuous Wavelet Transforms -- Generalized Frames: Key to Analysis and Synthesis -- Discrete Time-Frequency Analysis and Sampling -- Discrete Time-Scale Analysis -- Multiresolution Analysis -- Daubechies’ Orthonormal Wavelet Bases -- Part II: Physical Wavelets -- Introduction to Wavelet Electromagnetics -- Applications to Radar and Scattering -- Wavelet Acoustics -- References -- Index En línea: http://dx.doi.org/10.1007/978-0-8176-8111-1 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33104 A Friendly Guide to Wavelets [documento electrónico] / Gerald Kaiser ; SpringerLink (Online service) . - Boston : Birkhäuser Boston, 2011 . - XX, 300 p. 33 illus : online resource. - (Modern Birkhäuser Classics) .
ISBN : 978-0-8176-8111-1
Idioma : Inglés (eng)
Palabras clave: Mathematics Fourier analysis Applied mathematics Engineering Physics Applications of Signal, Image and Speech Processing Mathematical Methods in Analysis Clasificación: 51 Matemáticas Resumen: I wholeheartedly recommend this book for a solid and friendly introduction to wavelets, for anyone who is comfortable with the mathematics required of undergraduate electrical engineers. The book's appeal is that it covers all the fundamental concepts of wavelets in an elegant, straightforward way. It offers truly enjoyable (friendly!) mathematical exposition that is rich in intuitive explanations, as well as clean, direct, and clear in its theoretical developments. I found Kaiser's straightforward end-of-chapter exercises excellent...Kaiser has written an excellent introduction to the fundamental concepts of wavelets. For a book of its length and purpose, I think it should be essentially unbeatable for a long time. —Proceedings of the IEEE It is well produced and certainly readable...This material should present no difficulty for fourth-year undergraduates...It also will be useful to advanced workers in that it presents a different approach to wavelet theory from the usual one. —Computing Reviews I found this to be an excellent book. It is eminently more readable than the books...which might be considered the principal alternatives for textbooks on wavelets. —Physics Today This volume is probably the most gentle introduction to wavelet theory on the market. As such, it responds to a significant need. The intended audience will profit from the motivation and common-sense explanations in the text. Ultimately, it may lead many readers, who may not otherwise have been able to do so, to go further into wavelet theory, Fourier analysis, and signal processing. —SIAM Review The first half of the book is appropriately named. It is a well-written, nicely organized exposition...a welcome addition to the literature. The second part of the book introduces the concept of electromagnetic wavelets...This theory promises to have many other applications and could well lead to new ways of studying these topics. This book has a number of unique features which...makes it particularly valuable for newcomers to the field. —Mathematical Reviews The book is indeed what its title promises: A friendly guide to wavelets...In short, Kaiser's book is excellently written and can be considered as one of the best textbooks on this topic presently available...it will enjoy wide distribution among mathematicians and physicists interested in wavelet analysis. —Internationale Mathematische Nachrichten For additional review samples and related material, please visit the author's website at www.wavelets.com Nota de contenido: Preface -- Suggestions to the Reader -- Symbols, Conventions, and Transforms -- Part I: Basic Wavelet Analysis. Preliminaries: Background and Notation -- Windowed Fourier Transforms -- Continuous Wavelet Transforms -- Generalized Frames: Key to Analysis and Synthesis -- Discrete Time-Frequency Analysis and Sampling -- Discrete Time-Scale Analysis -- Multiresolution Analysis -- Daubechies’ Orthonormal Wavelet Bases -- Part II: Physical Wavelets -- Introduction to Wavelet Electromagnetics -- Applications to Radar and Scattering -- Wavelet Acoustics -- References -- Index En línea: http://dx.doi.org/10.1007/978-0-8176-8111-1 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33104 Ejemplares
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Título : Geometry and Spectra of Compact Riemann Surfaces Tipo de documento: documento electrónico Autores: Peter Buser ; SpringerLink (Online service) Editorial: Boston : Birkhäuser Boston Fecha de publicación: 2010 Colección: Modern Birkhäuser Classics Número de páginas: XIV, 456 p. 145 illus Il.: online resource ISBN/ISSN/DL: 978-0-8176-4992-0 Idioma : Inglés (eng) Palabras clave: Mathematics Algebra Algebraic geometry Functions of complex variables Geometry Several Complex Variables and Analytic Spaces Clasificación: 51 Matemáticas Resumen: This classic monograph is a self-contained introduction to the geometry of Riemann surfaces of constant curvature –1 and their length and eigenvalue spectra. It focuses on two subjects: the geometric theory of compact Riemann surfaces of genus greater than one, and the relationship of the Laplace operator with the geometry of such surfaces. The first part of the book is written in textbook form at the graduate level, with only minimal requisites in either differential geometry or complex Riemann surface theory. The second part of the book is a self-contained introduction to the spectrum of the Laplacian based on the heat equation. Later chapters deal with recent developments on isospectrality, Sunada’s construction, a simplified proof of Wolpert’s theorem, and an estimate of the number of pairwise isospectral non-isometric examples which depends only on genus. Researchers and graduate students interested in compact Riemann surfaces will find this book a useful reference. Anyone familiar with the author's hands-on approach to Riemann surfaces will be gratified by both the breadth and the depth of the topics considered here. The exposition is also extremely clear and thorough. Anyone not familiar with the author's approach is in for a real treat. — Mathematical Reviews This is a thick and leisurely book which will repay repeated study with many pleasant hours – both for the beginner and the expert. It is fortunately more or less self-contained, which makes it easy to read, and it leads one from essential mathematics to the “state of the art” in the theory of the Laplace–Beltrami operator on compact Riemann surfaces. Although it is not encyclopedic, it is so rich in information and ideas … the reader will be grateful for what has been included in this very satisfying book. —Bulletin of the AMS The book is very well written and quite accessible; there is an excellent bibliography at the end. —Zentralblatt MATH Nota de contenido: Hyperbolic Structures -- Trigonometry -- Y-Pieces and Twist Parameters -- The Collar Theorem -- Bers’ Constant and the Hairy Torus -- The Teichmüller Space -- The Spectrum of the Laplacian -- Small Eigenvalues -- Closed Geodesics and Huber’s Theorem -- Wolpert’s Theorem -- Sunada’s Theorem -- Examples of Isospectral Riemann Surfaces -- The Size of Isospectral Families -- Perturbations of the Laplacian in Teichmüller Space En línea: http://dx.doi.org/10.1007/978-0-8176-4992-0 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33566 Geometry and Spectra of Compact Riemann Surfaces [documento electrónico] / Peter Buser ; SpringerLink (Online service) . - Boston : Birkhäuser Boston, 2010 . - XIV, 456 p. 145 illus : online resource. - (Modern Birkhäuser Classics) .
ISBN : 978-0-8176-4992-0
Idioma : Inglés (eng)
Palabras clave: Mathematics Algebra Algebraic geometry Functions of complex variables Geometry Several Complex Variables and Analytic Spaces Clasificación: 51 Matemáticas Resumen: This classic monograph is a self-contained introduction to the geometry of Riemann surfaces of constant curvature –1 and their length and eigenvalue spectra. It focuses on two subjects: the geometric theory of compact Riemann surfaces of genus greater than one, and the relationship of the Laplace operator with the geometry of such surfaces. The first part of the book is written in textbook form at the graduate level, with only minimal requisites in either differential geometry or complex Riemann surface theory. The second part of the book is a self-contained introduction to the spectrum of the Laplacian based on the heat equation. Later chapters deal with recent developments on isospectrality, Sunada’s construction, a simplified proof of Wolpert’s theorem, and an estimate of the number of pairwise isospectral non-isometric examples which depends only on genus. Researchers and graduate students interested in compact Riemann surfaces will find this book a useful reference. Anyone familiar with the author's hands-on approach to Riemann surfaces will be gratified by both the breadth and the depth of the topics considered here. The exposition is also extremely clear and thorough. Anyone not familiar with the author's approach is in for a real treat. — Mathematical Reviews This is a thick and leisurely book which will repay repeated study with many pleasant hours – both for the beginner and the expert. It is fortunately more or less self-contained, which makes it easy to read, and it leads one from essential mathematics to the “state of the art” in the theory of the Laplace–Beltrami operator on compact Riemann surfaces. Although it is not encyclopedic, it is so rich in information and ideas … the reader will be grateful for what has been included in this very satisfying book. —Bulletin of the AMS The book is very well written and quite accessible; there is an excellent bibliography at the end. —Zentralblatt MATH Nota de contenido: Hyperbolic Structures -- Trigonometry -- Y-Pieces and Twist Parameters -- The Collar Theorem -- Bers’ Constant and the Hairy Torus -- The Teichmüller Space -- The Spectrum of the Laplacian -- Small Eigenvalues -- Closed Geodesics and Huber’s Theorem -- Wolpert’s Theorem -- Sunada’s Theorem -- Examples of Isospectral Riemann Surfaces -- The Size of Isospectral Families -- Perturbations of the Laplacian in Teichmüller Space En línea: http://dx.doi.org/10.1007/978-0-8176-4992-0 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33566 Ejemplares
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Título : A History of Algebraic and Differential Topology, 1900 - 1960 Tipo de documento: documento electrónico Autores: Jean Dieudonné ; SpringerLink (Online service) Editorial: Boston : Birkhäuser Boston Fecha de publicación: 2009 Colección: Modern Birkhäuser Classics Número de páginas: XXII, 648 p Il.: online resource ISBN/ISSN/DL: 978-0-8176-4907-4 Idioma : Inglés (eng) Palabras clave: Mathematics Differential geometry History Algebraic topology Topology Geometry of Mathematical Sciences Clasificación: 51 Matemáticas Resumen: Since the early part of the 20th century, topology has gradually spread to many other branches of mathematics, and this book demonstrates how the subject continues to play a central role in the field. Written by a world-renowned mathematician, this classic text traces the history of algebraic topology beginning with its creation in the early 1900s and describes in detail the important theories that were discovered before 1960. Through the work of Poincaré, de Rham, Cartan, Hureqicz, and many others, this historical book also focuses on the emergence of new ideas and methods that have led 21st-century mathematicians towards new research directions. ***************************** This book is a well-informed and detailed analysis of the problems and development of algebraic topology, from Poincaré and Brouwer to Serre, Adams, and Thom. The author has examined each significant paper along this route and describes the steps and strategy of its proofs and its relation to other work. Previously, the history of the many technical developments of 20th-century mathematics had seemed to present insuperable obstacles to scholarship. This book demonstrates in the case of topology how these obstacles can be overcome, with enlightening results.... Within its chosen boundaries the coverage of this book is superb. Read it! —MathSciNet [The author] traces the development of algebraic and differential topology from the innovative work by Poincaré at the turn of the century to the period around 1960. [He] has given a superb account of the growth of these fields.… The details are interwoven with the narrative in a very pleasant fashion.… [The author] has previous written histories of functional analysis and of algebraic geometry, but neither book was on such a grand scale as this one. He has made it possible to trace the important steps in the growth of algebraic and differential topology, and to admire the hard work and major advances made by the founders. —Zentralblatt MATH Nota de contenido: Simplicia1 Techniques and Homology -- The Work of Poincar#x00E9; -- The Build-Up of #x201C;Classical#x201D; Homology -- The Beginnings of Differential Topology -- The Various Homology and Cohomology Theories -- The First Applications of Simplicia1 Methods and of Homology -- The Concept of Degree -- Dimension Theory and Separation Theorems -- Fixed Points -- Local Homological Properties -- Quotient Spaces and Their Homology -- Homolagy of Groups and Homogeneous Spaces -- Applications of Homology to Geometry and Analysis -- Homotopy and its Relution to Homology -- Fundamental Group and Covering Spaces -- Elementary Notions and Early Results in Homotopy Theory -- Fibrations -- Homology of Fibrations -- Sophisticated Relations between Homotopy and Homology -- Cohomology Operations -- Generalized Homology and Cohomology En línea: http://dx.doi.org/10.1007/978-0-8176-4907-4 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33952 A History of Algebraic and Differential Topology, 1900 - 1960 [documento electrónico] / Jean Dieudonné ; SpringerLink (Online service) . - Boston : Birkhäuser Boston, 2009 . - XXII, 648 p : online resource. - (Modern Birkhäuser Classics) .
ISBN : 978-0-8176-4907-4
Idioma : Inglés (eng)
Palabras clave: Mathematics Differential geometry History Algebraic topology Topology Geometry of Mathematical Sciences Clasificación: 51 Matemáticas Resumen: Since the early part of the 20th century, topology has gradually spread to many other branches of mathematics, and this book demonstrates how the subject continues to play a central role in the field. Written by a world-renowned mathematician, this classic text traces the history of algebraic topology beginning with its creation in the early 1900s and describes in detail the important theories that were discovered before 1960. Through the work of Poincaré, de Rham, Cartan, Hureqicz, and many others, this historical book also focuses on the emergence of new ideas and methods that have led 21st-century mathematicians towards new research directions. ***************************** This book is a well-informed and detailed analysis of the problems and development of algebraic topology, from Poincaré and Brouwer to Serre, Adams, and Thom. The author has examined each significant paper along this route and describes the steps and strategy of its proofs and its relation to other work. Previously, the history of the many technical developments of 20th-century mathematics had seemed to present insuperable obstacles to scholarship. This book demonstrates in the case of topology how these obstacles can be overcome, with enlightening results.... Within its chosen boundaries the coverage of this book is superb. Read it! —MathSciNet [The author] traces the development of algebraic and differential topology from the innovative work by Poincaré at the turn of the century to the period around 1960. [He] has given a superb account of the growth of these fields.… The details are interwoven with the narrative in a very pleasant fashion.… [The author] has previous written histories of functional analysis and of algebraic geometry, but neither book was on such a grand scale as this one. He has made it possible to trace the important steps in the growth of algebraic and differential topology, and to admire the hard work and major advances made by the founders. —Zentralblatt MATH Nota de contenido: Simplicia1 Techniques and Homology -- The Work of Poincar#x00E9; -- The Build-Up of #x201C;Classical#x201D; Homology -- The Beginnings of Differential Topology -- The Various Homology and Cohomology Theories -- The First Applications of Simplicia1 Methods and of Homology -- The Concept of Degree -- Dimension Theory and Separation Theorems -- Fixed Points -- Local Homological Properties -- Quotient Spaces and Their Homology -- Homolagy of Groups and Homogeneous Spaces -- Applications of Homology to Geometry and Analysis -- Homotopy and its Relution to Homology -- Fundamental Group and Covering Spaces -- Elementary Notions and Early Results in Homotopy Theory -- Fibrations -- Homology of Fibrations -- Sophisticated Relations between Homotopy and Homology -- Cohomology Operations -- Generalized Homology and Cohomology En línea: http://dx.doi.org/10.1007/978-0-8176-4907-4 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33952 Ejemplares
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Título : Hyperbolic Manifolds and Discrete Groups Tipo de documento: documento electrónico Autores: Michael Kapovich ; SpringerLink (Online service) Editorial: Boston : Birkhäuser Boston Fecha de publicación: 2010 Colección: Modern Birkhäuser Classics Número de páginas: XXVI, 470 p. 78 illus Il.: online resource ISBN/ISSN/DL: 978-0-8176-4913-5 Idioma : Inglés (eng) Palabras clave: Mathematics Group theory Geometry Topology Manifolds (Mathematics) Complex manifolds Theory and Generalizations Cell Complexes (incl. Diff.Topology) Clasificación: 51 Matemáticas Resumen: This classic book is at the crossroads of several branches of mathematics: hyperbolic geometry, discrete groups, 3-dimensional topology, geometric group theory, and complex analysis. The main focus throughout the text is on Thurston’s hyperbolization theorem, one of the central results of 3-dimensional topology that has completely changed the landscape of the field. The book contains a number of open problems and conjectures related to the hyperbolization theorem as well as rich discussions on related topics including geometric structures on 3-manifolds, higher dimensional negatively curved manifolds, and hyperbolic groups. Featuring beautiful illustrations, a rich set of examples, numerous exercises, and an extensive bibliography and index, Hyperbolic Manifolds and Discrete Groups continues to serve as an ideal graduate text and comprehensive reference. The book is very clearly written and fairly self-contained. It will be useful to researchers and advanced graduate students in the field and can serve as an ideal guide to Thurston's work and its recent developments. ---Mathematical Reviews Beyond the hyperbolization theorem, this is an important book which had to be written; some parts are still technical and will certainly be streamlined and shortened in the next years, but together with Otal's work a complete published proof of the hyperbolization theorem is finally available. Apart from the proof itself, the book contains a lot of material which will be useful for various other directions of research. ---Zentralbatt MATH This book can act as source material for a postgraduate course and as a reference text on the topic as the references are full and extensive. ... The text is self-contained and very well illustrated. ---ASLIB Book Guide Nota de contenido: Three-Dimensional Topology -- Thurston Norm -- Geometry of Hyperbolic Space -- Kleinian Groups -- Teichmüller Theory of Riemann Surfaces -- to Orbifold Theory -- Complex Projective Structures -- Sociology of Kleinian Groups -- Ultralimits of Metric Spaces -- to Group Actions on Trees -- Laminations, Foliations, and Trees -- Rips Theory -- Brooks’ Theorem and Circle Packings -- Pleated Surfaces and Ends of Hyperbolic Manifolds -- Outline of the Proof of the Hyperbolization Theorem -- Reduction to the Bounded Image Theorem -- The Bounded Image Theorem -- Hyperbolization of Fibrations -- The Orbifold Trick -- Beyond the Hyperbolization Theorem En línea: http://dx.doi.org/10.1007/978-0-8176-4913-5 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33552 Hyperbolic Manifolds and Discrete Groups [documento electrónico] / Michael Kapovich ; SpringerLink (Online service) . - Boston : Birkhäuser Boston, 2010 . - XXVI, 470 p. 78 illus : online resource. - (Modern Birkhäuser Classics) .
ISBN : 978-0-8176-4913-5
Idioma : Inglés (eng)
Palabras clave: Mathematics Group theory Geometry Topology Manifolds (Mathematics) Complex manifolds Theory and Generalizations Cell Complexes (incl. Diff.Topology) Clasificación: 51 Matemáticas Resumen: This classic book is at the crossroads of several branches of mathematics: hyperbolic geometry, discrete groups, 3-dimensional topology, geometric group theory, and complex analysis. The main focus throughout the text is on Thurston’s hyperbolization theorem, one of the central results of 3-dimensional topology that has completely changed the landscape of the field. The book contains a number of open problems and conjectures related to the hyperbolization theorem as well as rich discussions on related topics including geometric structures on 3-manifolds, higher dimensional negatively curved manifolds, and hyperbolic groups. Featuring beautiful illustrations, a rich set of examples, numerous exercises, and an extensive bibliography and index, Hyperbolic Manifolds and Discrete Groups continues to serve as an ideal graduate text and comprehensive reference. The book is very clearly written and fairly self-contained. It will be useful to researchers and advanced graduate students in the field and can serve as an ideal guide to Thurston's work and its recent developments. ---Mathematical Reviews Beyond the hyperbolization theorem, this is an important book which had to be written; some parts are still technical and will certainly be streamlined and shortened in the next years, but together with Otal's work a complete published proof of the hyperbolization theorem is finally available. Apart from the proof itself, the book contains a lot of material which will be useful for various other directions of research. ---Zentralbatt MATH This book can act as source material for a postgraduate course and as a reference text on the topic as the references are full and extensive. ... The text is self-contained and very well illustrated. ---ASLIB Book Guide Nota de contenido: Three-Dimensional Topology -- Thurston Norm -- Geometry of Hyperbolic Space -- Kleinian Groups -- Teichmüller Theory of Riemann Surfaces -- to Orbifold Theory -- Complex Projective Structures -- Sociology of Kleinian Groups -- Ultralimits of Metric Spaces -- to Group Actions on Trees -- Laminations, Foliations, and Trees -- Rips Theory -- Brooks’ Theorem and Circle Packings -- Pleated Surfaces and Ends of Hyperbolic Manifolds -- Outline of the Proof of the Hyperbolization Theorem -- Reduction to the Bounded Image Theorem -- The Bounded Image Theorem -- Hyperbolization of Fibrations -- The Orbifold Trick -- Beyond the Hyperbolization Theorem En línea: http://dx.doi.org/10.1007/978-0-8176-4913-5 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33552 Ejemplares
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