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Título : Differential Topology Tipo de documento: documento electrónico Autores: SpringerLink (Online service) ; Villani, Vinicio Editorial: Berlin, Heidelberg : Springer Berlin Heidelberg Fecha de publicación: 2011 Colección: C.I.M.E. Summer Schools num. 73 Número de páginas: 159 p Il.: online resource ISBN/ISSN/DL: 978-3-642-11102-0 Idioma : Inglés (eng) Palabras clave: Mathematics Manifolds (Mathematics) Complex manifolds and Cell Complexes (incl. Diff.Topology) Clasificación: 51 Matemáticas Resumen: A. Banyaga: On the group of diffeomorphisms preserving an exact symplectic.- G.A. Fredricks: Some remarks on Cauchy-Riemann structures.- A. Haefliger: Differentiable Cohomology.- J.N. Mather: On the homology of Haefliger’s classifying space.- P. Michor: Manifolds of differentiable maps.- V. Poenaru: Some remarks on low-dimensional topology and immersion theory.- F. Sergeraert: La classe de cobordisme des feuilletages de Reeb de S3 est nulle.- G. Wallet: Invariant de Godbillon-Vey et difféomorphismes commutants Nota de contenido: A. Banyaga: On the group of diffeomorphisms preserving an exact symplectic -- G.A. Fredricks: Some remarks on Cauchy-Riemann structures -- A. Haefliger: Differentiable Cohomology -- J.N. Mather: On the homology of Haefliger’s classifying space -- P. Michor: Manifolds of differentiable maps -- V. Poenaru: Some remarks on low-dimensional topology and immersion theory -- F. Sergeraert: La classe de cobordisme des feuilletages de Reeb de S3 est nulle -- G. Wallet: Invariant de Godbillon-Vey et difféomorphismes commutants En línea: http://dx.doi.org/10.1007/978-3-642-11102-0 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33350 Differential Topology [documento electrónico] / SpringerLink (Online service) ; Villani, Vinicio . - Berlin, Heidelberg : Springer Berlin Heidelberg, 2011 . - 159 p : online resource. - (C.I.M.E. Summer Schools; 73) .
ISBN : 978-3-642-11102-0
Idioma : Inglés (eng)
Palabras clave: Mathematics Manifolds (Mathematics) Complex manifolds and Cell Complexes (incl. Diff.Topology) Clasificación: 51 Matemáticas Resumen: A. Banyaga: On the group of diffeomorphisms preserving an exact symplectic.- G.A. Fredricks: Some remarks on Cauchy-Riemann structures.- A. Haefliger: Differentiable Cohomology.- J.N. Mather: On the homology of Haefliger’s classifying space.- P. Michor: Manifolds of differentiable maps.- V. Poenaru: Some remarks on low-dimensional topology and immersion theory.- F. Sergeraert: La classe de cobordisme des feuilletages de Reeb de S3 est nulle.- G. Wallet: Invariant de Godbillon-Vey et difféomorphismes commutants Nota de contenido: A. Banyaga: On the group of diffeomorphisms preserving an exact symplectic -- G.A. Fredricks: Some remarks on Cauchy-Riemann structures -- A. Haefliger: Differentiable Cohomology -- J.N. Mather: On the homology of Haefliger’s classifying space -- P. Michor: Manifolds of differentiable maps -- V. Poenaru: Some remarks on low-dimensional topology and immersion theory -- F. Sergeraert: La classe de cobordisme des feuilletages de Reeb de S3 est nulle -- G. Wallet: Invariant de Godbillon-Vey et difféomorphismes commutants En línea: http://dx.doi.org/10.1007/978-3-642-11102-0 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33350 Ejemplares
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Título : Simplicial Structures in Topology Tipo de documento: documento electrónico Autores: Ferrario, Davide L ; SpringerLink (Online service) ; Piccinini, Renzo A Editorial: New York, NY : Springer New York Fecha de publicación: 2011 Otro editor: Imprint: Springer Colección: CMS Books in Mathematics, Ouvrages de mathématiques de la SMC, ISSN 1613-5237 Número de páginas: XVI, 243 p Il.: online resource ISBN/ISSN/DL: 978-1-4419-7236-1 Idioma : Inglés (eng) Palabras clave: Mathematics Topology Algebraic topology Manifolds (Mathematics) Complex manifolds and Cell Complexes (incl. Diff.Topology) Clasificación: 51 Matemáticas Resumen: Simplicial Structures in Topology provides a clear and comprehensive introduction to the subject. Ideas are developed in the first four chapters. The fifth chapter studies closed surfaces and gives their classification. The last chapter of the book is devoted to homotopy groups, which are used in a short introduction on obstruction theory. The text is more in tune with the original development of algebraic topology as given by Henri Poincaré (singular homology is not discussed). Illustrative examples throughout and extensive exercises at the end of each chapter for practice enhance the text. Advanced undergraduate and beginning graduate students will benefit from this book. Researchers and professionals interested in topology and applications of mathematics will also find this book useful Nota de contenido: Preface -- Fundamental Concepts -- Simplicial Complexes -- Homology of Polyhedra -- Cohonology -- Triangulable Manifolds -- Homotopy Groups -- Bibliography -- Index En línea: http://dx.doi.org/10.1007/978-1-4419-7236-1 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33156 Simplicial Structures in Topology [documento electrónico] / Ferrario, Davide L ; SpringerLink (Online service) ; Piccinini, Renzo A . - New York, NY : Springer New York : Imprint: Springer, 2011 . - XVI, 243 p : online resource. - (CMS Books in Mathematics, Ouvrages de mathématiques de la SMC, ISSN 1613-5237) .
ISBN : 978-1-4419-7236-1
Idioma : Inglés (eng)
Palabras clave: Mathematics Topology Algebraic topology Manifolds (Mathematics) Complex manifolds and Cell Complexes (incl. Diff.Topology) Clasificación: 51 Matemáticas Resumen: Simplicial Structures in Topology provides a clear and comprehensive introduction to the subject. Ideas are developed in the first four chapters. The fifth chapter studies closed surfaces and gives their classification. The last chapter of the book is devoted to homotopy groups, which are used in a short introduction on obstruction theory. The text is more in tune with the original development of algebraic topology as given by Henri Poincaré (singular homology is not discussed). Illustrative examples throughout and extensive exercises at the end of each chapter for practice enhance the text. Advanced undergraduate and beginning graduate students will benefit from this book. Researchers and professionals interested in topology and applications of mathematics will also find this book useful Nota de contenido: Preface -- Fundamental Concepts -- Simplicial Complexes -- Homology of Polyhedra -- Cohonology -- Triangulable Manifolds -- Homotopy Groups -- Bibliography -- Index En línea: http://dx.doi.org/10.1007/978-1-4419-7236-1 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33156 Ejemplares
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Título : String Topology and Cyclic Homology Tipo de documento: documento electrónico Autores: Cohen, Ralph L ; SpringerLink (Online service) ; Hess, Kathryn ; Voronov, Alexander A Editorial: Basel : Birkhäuser Basel Fecha de publicación: 2006 Colección: Advanced Courses in Mathematics CRM Barcelona, Centre de Recerca Matemàtica Número de páginas: VII, 163 p Il.: online resource ISBN/ISSN/DL: 978-3-7643-7388-7 Idioma : Inglés (eng) Palabras clave: Mathematics Algebraic topology Manifolds (Mathematics) Complex manifolds Physics Topology and Cell Complexes (incl. Diff.Topology) Mathematical Methods in Clasificación: 51 Matemáticas Resumen: The subject of this book is string topology, Hochschild and cyclic homology. The first part consists of an excellent exposition of various approaches to string topology and the Chas-Sullivan loop product. The second gives a complete and clear construction of an algebraic model for computing topological cyclic homology. The book provides many references for the reader wishing to learn more about the subject, to which it gives a perfect introduction. It is therefore suitable for both graduate students and established researchers. It is certainly the best source of much information that was until now available only to specialists and covers material from the elementary bases to the most recent developments Nota de contenido: Notes on String Topology -- Intersection theory in loop spaces -- The cacti operad -- Field theoretic properties of string topology -- A Morse theoretic viewpoint -- Brane topology -- An Algebraic Model for Mod 2 Topological Cyclic Homology -- Preliminaries -- Free loop spaces -- Homotopy orbit spaces -- A model for mod 2 topological cyclic homology En línea: http://dx.doi.org/10.1007/3-7643-7388-1 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=35003 String Topology and Cyclic Homology [documento electrónico] / Cohen, Ralph L ; SpringerLink (Online service) ; Hess, Kathryn ; Voronov, Alexander A . - Basel : Birkhäuser Basel, 2006 . - VII, 163 p : online resource. - (Advanced Courses in Mathematics CRM Barcelona, Centre de Recerca Matemàtica) .
ISBN : 978-3-7643-7388-7
Idioma : Inglés (eng)
Palabras clave: Mathematics Algebraic topology Manifolds (Mathematics) Complex manifolds Physics Topology and Cell Complexes (incl. Diff.Topology) Mathematical Methods in Clasificación: 51 Matemáticas Resumen: The subject of this book is string topology, Hochschild and cyclic homology. The first part consists of an excellent exposition of various approaches to string topology and the Chas-Sullivan loop product. The second gives a complete and clear construction of an algebraic model for computing topological cyclic homology. The book provides many references for the reader wishing to learn more about the subject, to which it gives a perfect introduction. It is therefore suitable for both graduate students and established researchers. It is certainly the best source of much information that was until now available only to specialists and covers material from the elementary bases to the most recent developments Nota de contenido: Notes on String Topology -- Intersection theory in loop spaces -- The cacti operad -- Field theoretic properties of string topology -- A Morse theoretic viewpoint -- Brane topology -- An Algebraic Model for Mod 2 Topological Cyclic Homology -- Preliminaries -- Free loop spaces -- Homotopy orbit spaces -- A model for mod 2 topological cyclic homology En línea: http://dx.doi.org/10.1007/3-7643-7388-1 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=35003 Ejemplares
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Título : An Introduction to Manifolds Tipo de documento: documento electrónico Autores: Tu, Loring W ; SpringerLink (Online service) Editorial: New York, NY : Springer New York Fecha de publicación: 2011 Colección: Universitext, ISSN 0172-5939 Número de páginas: XVIII, 410 p. 124 illus., 1 illus. in color Il.: online resource ISBN/ISSN/DL: 978-1-4419-7400-6 Idioma : Inglés (eng) Palabras clave: Mathematics Global analysis (Mathematics) Manifolds Differential geometry Complex manifolds and Cell Complexes (incl. Diff.Topology) Analysis on Geometry Clasificación: 51 Matemáticas Resumen: Manifolds, the higher-dimensional analogues of smooth curves and surfaces, are fundamental objects in modern mathematics. Combining aspects of algebra, topology, and analysis, manifolds have also been applied to classical mechanics, general relativity, and quantum field theory. In this streamlined introduction to the subject, the theory of manifolds is presented with the aim of helping the reader achieve a rapid mastery of the essential topics. By the end of the book the reader should be able to compute, at least for simple spaces, one of the most basic topological invariants of a manifold, its de Rham cohomology. Along the way the reader acquires the knowledge and skills necessary for further study of geometry and topology. The second edition contains fifty pages of new material. Many passages have been rewritten, proofs simplified, and new examples and exercises added. This work may be used as a textbook for a one-semester graduate or advanced undergraduate course, as well as by students engaged in self-study. The requisite point-set topology is included in an appendix of twenty-five pages; other appendices review facts from real analysis and linear algebra. Hints and solutions are provided to many of the exercises and problems. Requiring only minimal undergraduate prerequisites, "An Introduction to Manifolds" is also an excellent foundation for the author's publication with Raoul Bott, "Differential Forms in Algebraic Topology." Nota de contenido: Preface to the Second Edition -- Preface to the First Edition -- Chapter 1. Euclidean Spaces -- Chapter 2. Manifolds -- Chapter 3. The Tangent Space -- Chapter 4. Lie Groups and Lie Algebras.-Chapter 5. Differential Forms -- Chapter 6. Integration.-Chapter 7. De Rham Theory -- Appendices -- A. Point-Set Topology -- B. The Inverse Function Theorem on R(N) and Related Results -- C. Existence of a Partition of Unity in General -- D. Linear Algebra -- E. Quaternions and the Symplectic Group -- Solutions to Selected Exercises -- Hints and Solutions to Selected End-of-Section Problems -- List of Symbols -- References -- Index En línea: http://dx.doi.org/10.1007/978-1-4419-7400-6 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33161 An Introduction to Manifolds [documento electrónico] / Tu, Loring W ; SpringerLink (Online service) . - New York, NY : Springer New York, 2011 . - XVIII, 410 p. 124 illus., 1 illus. in color : online resource. - (Universitext, ISSN 0172-5939) .
ISBN : 978-1-4419-7400-6
Idioma : Inglés (eng)
Palabras clave: Mathematics Global analysis (Mathematics) Manifolds Differential geometry Complex manifolds and Cell Complexes (incl. Diff.Topology) Analysis on Geometry Clasificación: 51 Matemáticas Resumen: Manifolds, the higher-dimensional analogues of smooth curves and surfaces, are fundamental objects in modern mathematics. Combining aspects of algebra, topology, and analysis, manifolds have also been applied to classical mechanics, general relativity, and quantum field theory. In this streamlined introduction to the subject, the theory of manifolds is presented with the aim of helping the reader achieve a rapid mastery of the essential topics. By the end of the book the reader should be able to compute, at least for simple spaces, one of the most basic topological invariants of a manifold, its de Rham cohomology. Along the way the reader acquires the knowledge and skills necessary for further study of geometry and topology. The second edition contains fifty pages of new material. Many passages have been rewritten, proofs simplified, and new examples and exercises added. This work may be used as a textbook for a one-semester graduate or advanced undergraduate course, as well as by students engaged in self-study. The requisite point-set topology is included in an appendix of twenty-five pages; other appendices review facts from real analysis and linear algebra. Hints and solutions are provided to many of the exercises and problems. Requiring only minimal undergraduate prerequisites, "An Introduction to Manifolds" is also an excellent foundation for the author's publication with Raoul Bott, "Differential Forms in Algebraic Topology." Nota de contenido: Preface to the Second Edition -- Preface to the First Edition -- Chapter 1. Euclidean Spaces -- Chapter 2. Manifolds -- Chapter 3. The Tangent Space -- Chapter 4. Lie Groups and Lie Algebras.-Chapter 5. Differential Forms -- Chapter 6. Integration.-Chapter 7. De Rham Theory -- Appendices -- A. Point-Set Topology -- B. The Inverse Function Theorem on R(N) and Related Results -- C. Existence of a Partition of Unity in General -- D. Linear Algebra -- E. Quaternions and the Symplectic Group -- Solutions to Selected Exercises -- Hints and Solutions to Selected End-of-Section Problems -- List of Symbols -- References -- Index En línea: http://dx.doi.org/10.1007/978-1-4419-7400-6 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33161 Ejemplares
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Título : An Invitation to Morse Theory Tipo de documento: documento electrónico Autores: Nicolaescu, Liviu ; SpringerLink (Online service) Editorial: New York, NY : Springer New York Fecha de publicación: 2011 Colección: Universitext, ISSN 0172-5939 Número de páginas: XVI, 353 p. 47 illus Il.: online resource ISBN/ISSN/DL: 978-1-4614-1105-5 Idioma : Inglés (eng) Palabras clave: Mathematics Global analysis (Mathematics) Manifolds Differential geometry Complex manifolds Analysis and on Geometry Cell Complexes (incl. Diff.Topology) Clasificación: 51 Matemáticas Resumen: This self-contained treatment of Morse theory focuses on applications and is intended for a graduate course on differential or algebraic topology. The book is divided into three conceptually distinct parts. The first part contains the foundations of Morse theory. The second part consists of applications of Morse theory over the reals, while the last part describes the basics and some applications of complex Morse theory, a.k.a. Picard-Lefschetz theory. This is the first textbook to include topics such as Morse-Smale flows, Floer homology, min-max theory, moment maps and equivariant cohomology, and complex Morse theory. The exposition is enhanced with examples, problems, and illustrations, and will be of interest to graduate students as well as researchers. The reader is expected to have some familiarity with cohomology theory and with the differential and integral calculus on smooth manifolds. Some features of the second edition include added applications, such as Morse theory and the curvature of knots, the cohomology of the moduli space of planar polygons, and the Duistermaat-Heckman formula. The second edition also includes a new chapter on Morse-Smale flows and Whitney stratifications, many new exercises, and various corrections from the first edition Nota de contenido: Preface -- Notations and Conventions -- 1 Morse Functions -- 2 The Topology of Morse Functions -- 3 Applications -- 4 Morse-Smale Flows and Whitney Stratifications -- 5 Basics of Complex Morse Theory -- 6 Exercises and Solutions -- References -- Index En línea: http://dx.doi.org/10.1007/978-1-4614-1105-5 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33234 An Invitation to Morse Theory [documento electrónico] / Nicolaescu, Liviu ; SpringerLink (Online service) . - New York, NY : Springer New York, 2011 . - XVI, 353 p. 47 illus : online resource. - (Universitext, ISSN 0172-5939) .
ISBN : 978-1-4614-1105-5
Idioma : Inglés (eng)
Palabras clave: Mathematics Global analysis (Mathematics) Manifolds Differential geometry Complex manifolds Analysis and on Geometry Cell Complexes (incl. Diff.Topology) Clasificación: 51 Matemáticas Resumen: This self-contained treatment of Morse theory focuses on applications and is intended for a graduate course on differential or algebraic topology. The book is divided into three conceptually distinct parts. The first part contains the foundations of Morse theory. The second part consists of applications of Morse theory over the reals, while the last part describes the basics and some applications of complex Morse theory, a.k.a. Picard-Lefschetz theory. This is the first textbook to include topics such as Morse-Smale flows, Floer homology, min-max theory, moment maps and equivariant cohomology, and complex Morse theory. The exposition is enhanced with examples, problems, and illustrations, and will be of interest to graduate students as well as researchers. The reader is expected to have some familiarity with cohomology theory and with the differential and integral calculus on smooth manifolds. Some features of the second edition include added applications, such as Morse theory and the curvature of knots, the cohomology of the moduli space of planar polygons, and the Duistermaat-Heckman formula. The second edition also includes a new chapter on Morse-Smale flows and Whitney stratifications, many new exercises, and various corrections from the first edition Nota de contenido: Preface -- Notations and Conventions -- 1 Morse Functions -- 2 The Topology of Morse Functions -- 3 Applications -- 4 Morse-Smale Flows and Whitney Stratifications -- 5 Basics of Complex Morse Theory -- 6 Exercises and Solutions -- References -- Index En línea: http://dx.doi.org/10.1007/978-1-4614-1105-5 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33234 Ejemplares
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