Complex Kleinian Groups / Angel Cano (2013)  

Público ISBD Título : Complex Kleinian Groups Tipo de documento: documento electrónico Autores: Angel Cano ; SpringerLink (Online service) ; Juan Pablo Navarrete ; Seade, José Editorial: Basel : Springer Basel Fecha de publicación: 2013 Otro editor: Imprint: Birkhäuser Colección: Progress in Mathematics, ISSN 0743-1643 num. 303 Número de páginas: XX, 272 p Il.: online resource ISBN/ISSN/DL: 978-3-0348-0481-3 Idioma : Inglés (eng) Palabras clave: Mathematics  Topological  groups  Lie  Dynamics  Ergodic  theory  Functions  of  complex  variables  Dynamical  Systems  and  Theory  Groups,  Groups  Several  Complex  Variables  Analytic  Spaces Clasificación: 51 Matemáticas Resumen: This monograph lays down the foundations of the theory of complex Kleinian groups, a “newborn” area of mathematics whose origin can be traced back to the work of Riemann, Poincaré, Picard and many others. Kleinian groups are, classically, discrete groups of conformal automorphisms of the Riemann sphere, and these can themselves be regarded as groups of holomorphic automorphisms of the complex projective line CP1. When we go into higher dimensions, there is a dichotomy: Should we look at conformal automorphisms of the n-sphere? or should we look at holomorphic automorphisms of higher dimensional complex projective spaces? These two theories differ in higher dimensions. In the first case we are talking about groups of isometries of real hyperbolic spaces, an area of mathematics with a long-standing tradition; in the second, about an area of mathematics that is still in its infancy, and this is the focus of study in this monograph. It brings together several important areas of mathematics, e.g. classical Kleinian group actions, complex hyperbolic geometry, crystallographic groups and the uniformization problem for complex manifolds Nota de contenido:   Preface -- Introduction -- Acknowledgments -- 1 A glance of the classical theory -- 2 Complex hyperbolic geometry -- 3 Complex Kleinian groups -- 4 Geometry and dynamics of automorphisms of P2C -- 5 Kleinian groups with a control group -- 6 The limit set in dimension two -- 7 On the dynamics of discrete subgroups of PU(n,1) -- 8 Projective orbifolds and dynamics in dimension two -- 9 Complex Schottky groups -- 10 Kleinian groups and twistor theory -- Bibliography -- Index.   En línea: http://dx.doi.org/10.1007/978-3-0348-0481-3 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=32420 Complex Kleinian Groups [documento electrónico] / Angel Cano ; SpringerLink (Online service) ; Juan Pablo Navarrete ; Seade, José . - Basel : Springer Basel : Imprint: Birkhäuser, 2013 . - XX, 272 p : online resource. - (Progress in Mathematics, ISSN 0743-1643; 303) . ISBN : 978-3-0348-0481-3 Idioma : Inglés (eng) Palabras clave: Mathematics  Topological  groups  Lie  Dynamics  Ergodic  theory  Functions  of  complex  variables  Dynamical  Systems  and  Theory  Groups,  Groups  Several  Complex  Variables  Analytic  Spaces Clasificación: 51 Matemáticas Resumen: This monograph lays down the foundations of the theory of complex Kleinian groups, a “newborn” area of mathematics whose origin can be traced back to the work of Riemann, Poincaré, Picard and many others. Kleinian groups are, classically, discrete groups of conformal automorphisms of the Riemann sphere, and these can themselves be regarded as groups of holomorphic automorphisms of the complex projective line CP1. When we go into higher dimensions, there is a dichotomy: Should we look at conformal automorphisms of the n-sphere? or should we look at holomorphic automorphisms of higher dimensional complex projective spaces? These two theories differ in higher dimensions. In the first case we are talking about groups of isometries of real hyperbolic spaces, an area of mathematics with a long-standing tradition; in the second, about an area of mathematics that is still in its infancy, and this is the focus of study in this monograph. It brings together several important areas of mathematics, e.g. classical Kleinian group actions, complex hyperbolic geometry, crystallographic groups and the uniformization problem for complex manifolds Nota de contenido:   Preface -- Introduction -- Acknowledgments -- 1 A glance of the classical theory -- 2 Complex hyperbolic geometry -- 3 Complex Kleinian groups -- 4 Geometry and dynamics of automorphisms of P2C -- 5 Kleinian groups with a control group -- 6 The limit set in dimension two -- 7 On the dynamics of discrete subgroups of PU(n,1) -- 8 Projective orbifolds and dynamics in dimension two -- 9 Complex Schottky groups -- 10 Kleinian groups and twistor theory -- Bibliography -- Index.   En línea: http://dx.doi.org/10.1007/978-3-0348-0481-3 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=32420

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Introduction to Classical Geometries / Ana Irene Ramírez Galarza (2007)  

Público ISBD Título : Introduction to Classical Geometries Tipo de documento: documento electrónico Autores: Ana Irene Ramírez Galarza ; SpringerLink (Online service) ; Seade, José Editorial: Basel : Birkhäuser Basel Fecha de publicación: 2007 Número de páginas: X, 220 p Il.: online resource ISBN/ISSN/DL: 978-3-7643-7518-8 Idioma : Inglés (eng) Palabras clave: Mathematics  Geometry  Mathematics,  general Clasificación: 51 Matemáticas Resumen: This book follows Felix Klein’s proposal of studying geometry by looking at the symmetries (or rigid motions) of the space in question. In this way the classical geometries are studied: Euclidean, affine, elliptic, projective and hyperbolic. For simplicity the focus is on the two-dimensional case, which is already rich enough, though some aspects of the 3- or n-dimensional geometries are included. Once plane geometry is well understood, it is much easier to go into higher dimensions. The fundamental ideas of the classical geometries are presented in a clear and elementary way, making them accessible to a wide audience, and relating them to more advanced topics in modern geometry, such as manifolds, Lie groups, the Gaussian curvature, group actions, and foliations. The book appeals to, and develops, the geometric intuition of the reader. The only prerequisites are calculus, linear algebra and basic analytic geometry. After studying the material, the reader will have a good understanding of basic geometry as well as a clear picture of the relations of this beautiful subject to other branches of mathematics. This is supported by more than 100 carefully chosen illustrations and a large number of exercises. While mainly addressed to students at advanced undergraduate level, the text can be of interest to anyone wanting to learn classical geometry Nota de contenido: Euclidean geometry -- Affine geometry -- Projective geometry -- Hyperbolic geometry -- Appendices En línea: http://dx.doi.org/10.1007/978-3-7643-7518-8 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34675 Introduction to Classical Geometries [documento electrónico] / Ana Irene Ramírez Galarza ; SpringerLink (Online service) ; Seade, José . - Basel : Birkhäuser Basel, 2007 . - X, 220 p : online resource. ISBN : 978-3-7643-7518-8 Idioma : Inglés (eng) Palabras clave: Mathematics  Geometry  Mathematics,  general Clasificación: 51 Matemáticas Resumen: This book follows Felix Klein’s proposal of studying geometry by looking at the symmetries (or rigid motions) of the space in question. In this way the classical geometries are studied: Euclidean, affine, elliptic, projective and hyperbolic. For simplicity the focus is on the two-dimensional case, which is already rich enough, though some aspects of the 3- or n-dimensional geometries are included. Once plane geometry is well understood, it is much easier to go into higher dimensions. The fundamental ideas of the classical geometries are presented in a clear and elementary way, making them accessible to a wide audience, and relating them to more advanced topics in modern geometry, such as manifolds, Lie groups, the Gaussian curvature, group actions, and foliations. The book appeals to, and develops, the geometric intuition of the reader. The only prerequisites are calculus, linear algebra and basic analytic geometry. After studying the material, the reader will have a good understanding of basic geometry as well as a clear picture of the relations of this beautiful subject to other branches of mathematics. This is supported by more than 100 carefully chosen illustrations and a large number of exercises. While mainly addressed to students at advanced undergraduate level, the text can be of interest to anyone wanting to learn classical geometry Nota de contenido: Euclidean geometry -- Affine geometry -- Projective geometry -- Hyperbolic geometry -- Appendices En línea: http://dx.doi.org/10.1007/978-3-7643-7518-8 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34675

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On the Topology of Isolated Singularities in Analytic Spaces / Seade, José (2006)  

Público ISBD Título : On the Topology of Isolated Singularities in Analytic Spaces Tipo de documento: documento electrónico Autores: Seade, José ; SpringerLink (Online service) Editorial: Basel : Birkhäuser Basel Fecha de publicación: 2006 Colección: Progress in Mathematics num. 241 Número de páginas: XIV, 238 p Il.: online resource ISBN/ISSN/DL: 978-3-7643-7395-5 Idioma : Inglés (eng) Palabras clave: Mathematics  Topological  groups  Lie  Functions  of  complex  variables  Differential  geometry  Algebraic  topology  a  Complex  Variable  Groups,  Groups  Geometry  Topology Clasificación: 51 Matemáticas Resumen: The aim of this book is to give an overview of selected topics on the topology of real and complex isolated singularities, with emphasis on its relations to other branches of geometry and topology. The first chapters are mostly devoted to complex singularities and a myriad of results spread in a vast literature, which are presented here in a unified way, accessible to non-specialists. Among the topics are the fibration theorems of Milnor; the relation with 3-dimensional Lie groups; exotic spheres; spin structures and 3-manifold invariants; the geometry of quadrics and Arnold's theorem which states that the complex projective plane modulo conjugation is the 4-sphere. The second part of the book studies pioneer work about real analytic singularities which arise from the topological and geometric study of holomorphic vector fields and foliations. In the low dimensional case these turn out to be related to fibred links in the 3-sphere defined by meromorphic functions. This provides new methods for constructing manifolds equipped with a rich geometry. The book is largely self-contained and serves a wide audience of graduate students, mathematicians and researchers interested in geometry and topology Nota de contenido: A Fast Trip Through the Classical Theory -- Motions in Plane Geometry and the 3-dimensional Brieskorn Manifolds -- 3-dimensional Lie Groups and Surface Singularities -- Within the Realm of the General Index Theorem -- On the Geometry and Topology of Quadrics in ??n -- Real Singularities and Complex Geometry -- Real Singularities with a Milnor Fibration -- Real Singularities and Open Book Decompositions of the 3-sphere En línea: http://dx.doi.org/10.1007/3-7643-7395-4 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=35006 On the Topology of Isolated Singularities in Analytic Spaces [documento electrónico] / Seade, José ; SpringerLink (Online service) . - Basel : Birkhäuser Basel, 2006 . - XIV, 238 p : online resource. - (Progress in Mathematics; 241) . ISBN : 978-3-7643-7395-5 Idioma : Inglés (eng) Palabras clave: Mathematics  Topological  groups  Lie  Functions  of  complex  variables  Differential  geometry  Algebraic  topology  a  Complex  Variable  Groups,  Groups  Geometry  Topology Clasificación: 51 Matemáticas Resumen: The aim of this book is to give an overview of selected topics on the topology of real and complex isolated singularities, with emphasis on its relations to other branches of geometry and topology. The first chapters are mostly devoted to complex singularities and a myriad of results spread in a vast literature, which are presented here in a unified way, accessible to non-specialists. Among the topics are the fibration theorems of Milnor; the relation with 3-dimensional Lie groups; exotic spheres; spin structures and 3-manifold invariants; the geometry of quadrics and Arnold's theorem which states that the complex projective plane modulo conjugation is the 4-sphere. The second part of the book studies pioneer work about real analytic singularities which arise from the topological and geometric study of holomorphic vector fields and foliations. In the low dimensional case these turn out to be related to fibred links in the 3-sphere defined by meromorphic functions. This provides new methods for constructing manifolds equipped with a rich geometry. The book is largely self-contained and serves a wide audience of graduate students, mathematicians and researchers interested in geometry and topology Nota de contenido: A Fast Trip Through the Classical Theory -- Motions in Plane Geometry and the 3-dimensional Brieskorn Manifolds -- 3-dimensional Lie Groups and Surface Singularities -- Within the Realm of the General Index Theorem -- On the Geometry and Topology of Quadrics in ??n -- Real Singularities and Complex Geometry -- Real Singularities with a Milnor Fibration -- Real Singularities and Open Book Decompositions of the 3-sphere En línea: http://dx.doi.org/10.1007/3-7643-7395-4 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=35006

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