Complex Kleinian Groups

Author : Angel Cano,Juan Pablo Navarrete,José Seade
Publisher : Springer Science & Business Media
Page : 288 pages
File Size : 40,9 Mb
Release : 2012-11-05
Category : Mathematics
ISBN : 9783034804813

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Complex Kleinian Groups by Angel Cano,Juan Pablo Navarrete,José Seade Pdf

This monograph lays down the foundations of the theory of complex Kleinian groups, a newly born area of mathematics whose origin traces 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 be regarded too as being groups of holomorphic automorphisms of the complex projective line CP1. When going 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 are different 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 case we are talking about an area of mathematics that still is in its childhood, and this is the focus of study in this monograph. This brings together several important areas of mathematics, as for instance classical Kleinian group actions, complex hyperbolic geometry, chrystallographic groups and the uniformization problem for complex manifolds.​

Author : Springer
Publisher : Unknown
Page : 294 pages
File Size : 45,8 Mb
Release : 2012-11-07
Category : Electronic
ISBN : 3034804822

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Complex Kleinian Groups by Springer Pdf

Author : Katsuhiko Matsuzaki,Masahiko Taniguchi
Publisher : Clarendon Press
Page : 265 pages
File Size : 55,6 Mb
Release : 1998-04-30
Category : Mathematics
ISBN : 9780191591204

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Hyperbolic Manifolds and Kleinian Groups by Katsuhiko Matsuzaki,Masahiko Taniguchi Pdf

A Kleinian group is a discrete subgroup of the isometry group of hyperbolic 3-space, which is also regarded as a subgroup of Möbius transformations in the complex plane. The present book is a comprehensive guide to theories of Kleinian groups from the viewpoints of hyperbolic geometry and complex analysis. After 1960, Ahlfors and Bers were the leading researchers of Kleinian groups and helped it to become an active area of complex analysis as a branch of Teichmüller theory. Later, Thurston brought a revolution to this area with his profound investigation of hyperbolic manifolds, and at the same time complex dynamical approach was strongly developed by Sullivan. This book provides fundamental results and important theorems which are needed for access to the frontiers of the theory from a modern viewpoint.

Author : Yair N. Minsky,Makoto Sakuma,Caroline Series
Publisher : Cambridge University Press
Page : 399 pages
File Size : 40,7 Mb
Release : 2006-06-19
Category : Mathematics
ISBN : 9781139447218

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Spaces of Kleinian Groups by Yair N. Minsky,Makoto Sakuma,Caroline Series Pdf

The subject of Kleinian groups and hyperbolic 3-manifolds is currently undergoing explosively fast development. This volume contains important expositions on topics such as topology and geometry of 3-manifolds, curve complexes, classical Ahlfors-Bers theory and computer explorations. Researchers in these and related areas will find much of interest here.

Author : D.M. Gallo,R.M. Porter
Publisher : Springer
Page : 126 pages
File Size : 41,6 Mb
Release : 2006-11-15
Category : Mathematics
ISBN : 9783540394266

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Kleinian Groups and Related Topics by D.M. Gallo,R.M. Porter Pdf

Author : Samuil Leĭbovich Krushkalʹ,Boris Nikolaevich Apanasov,Nikolaĭ Aleksandrovich Gusevskiĭ
Publisher : American Mathematical Soc.
Page : 212 pages
File Size : 51,5 Mb
Release : 1986
Category : Kleinian groups
ISBN : 9780821845165

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Kleinian Groups and Uniformization in Examples and Problems by Samuil Leĭbovich Krushkalʹ,Boris Nikolaevich Apanasov,Nikolaĭ Aleksandrovich Gusevskiĭ Pdf

Presents a unified exposition of the main areas and methods of the theory of Kleinian groups and the theory of uniformization of manifolds. This book lists the basic facts regarding Kleinian groups and serves as a general guide to the primary literature, particularly the Russian literature in the field.

Author : Michael Kapovich
Publisher : Springer Science & Business Media
Page : 470 pages
File Size : 41,6 Mb
Release : 2009-08-04
Category : Mathematics
ISBN : 9780817649135

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Hyperbolic Manifolds and Discrete Groups by Michael Kapovich Pdf

Hyperbolic Manifolds and Discrete Groups 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 the "Big Monster," i.e., on Thurston’s hyperbolization theorem, which has not only completely changes the landscape of 3-dimensinal topology and Kleinian group theory but is one of the central results of 3-dimensional topology. The book is fairly self-contained, replete with beautiful illustrations, a rich set of examples of key concepts, numerous exercises, and an extensive bibliography and index. It should serve as an ideal graduate course/seminar text or as a comprehensive reference.

Author : Samuil Leĭbovich Krushkalʹ,Boris Nikolaevich Apanasov,Nikolaĭ Aleksandrovich Gusevskiĭ
Publisher : Unknown
Page : 128 pages
File Size : 44,9 Mb
Release : 1986
Category : Kleinian groups
ISBN : 1470444763

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Kleinian Groups and Uniformization in Examples and Problems by Samuil Leĭbovich Krushkalʹ,Boris Nikolaevich Apanasov,Nikolaĭ Aleksandrovich Gusevskiĭ Pdf

Aimed at researchers, graduate students and undergraduates alike, this book presents a unified exposition of all the main areas and methods of the theory of Kleinian groups and the theory of uniformization of manifolds. The past 20 years have seen a rejuvenation of the field, due to the development of powerful new methods in topology, the theory of functions of several complex variables, and the theory of quasiconformal mappings. Thus this new book should provide a valuable resource, listing the basic facts regarding Kleinian groups and serving as a general guide to the primary literature, par.

Author : C. S. Aravinda,William M. Goldman, Krishnendu Gongopadhyay, Alexander Lubotzky, Mahan Mj,Anthony Weaver
Publisher : American Mathematical Soc.
Page : 369 pages
File Size : 51,5 Mb
Release : 2015-05-01
Category : Discrete groups
ISBN : 9780821898826

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Geometry, Groups and Dynamics by C. S. Aravinda,William M. Goldman, Krishnendu Gongopadhyay, Alexander Lubotzky, Mahan Mj,Anthony Weaver Pdf

This volume contains the proceedings of the ICTS Program: Groups, Geometry and Dynamics, held December 3-16, 2012, at CEMS, Almora, India. The activity was an academic tribute to Ravi S. Kulkarni on his turning seventy. Articles included in this volume, both introductory and advanced surveys, represent the broad area of geometry that encompasses a large portion of group theory (finite or otherwise) and dynamics in its proximity. These areas have been influenced by Kulkarni's ideas and are closely related to his work and contribution.

Author : L. Bers,I. Kra
Publisher : Springer
Page : 140 pages
File Size : 44,5 Mb
Release : 2006-11-15
Category : Mathematics
ISBN : 9783540377764

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A Crash Course on Kleinian Groups by L. Bers,I. Kra Pdf

Author : Vasileios Chousionis,Jeremy T. Tyson,Mariusz Urbanski
Publisher : American Mathematical Soc.
Page : 153 pages
File Size : 42,9 Mb
Release : 2020-09-28
Category : Mathematics
ISBN : 9781470442156

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Conformal Graph Directed Markov Systems on Carnot Groups by Vasileios Chousionis,Jeremy T. Tyson,Mariusz Urbanski Pdf

The authors develop a comprehensive theory of conformal graph directed Markov systems in the non-Riemannian setting of Carnot groups equipped with a sub-Riemannian metric. In particular, they develop the thermodynamic formalism and show that, under natural hypotheses, the limit set of an Carnot conformal GDMS has Hausdorff dimension given by Bowen's parameter. They illustrate their results for a variety of examples of both linear and nonlinear iterated function systems and graph directed Markov systems in such sub-Riemannian spaces. These include the Heisenberg continued fractions introduced by Lukyanenko and Vandehey as well as Kleinian and Schottky groups associated to the non-real classical rank one hyperbolic spaces.

Author : Mikhail Lyubich,John Willard Milnor
Publisher : American Mathematical Soc.
Page : 250 pages
File Size : 41,7 Mb
Release : 2001
Category : Foliations (Mathematics)
ISBN : 9780821819852

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Laminations and Foliations in Dynamics, Geometry and Topology by Mikhail Lyubich,John Willard Milnor Pdf

This volume is based on a conference held at SUNY, Stony Brook (NY). The concepts of laminations and foliations appear in a diverse number of fields, such as topology, geometry, analytic differential equations, holomorphic dynamics, and renormalization theory. Although these areas have developed deep relations, each has developed distinct research fields with little interaction among practitioners. The conference brought together the diverse points of view of researchers from different areas. This book includes surveys and research papers reflecting the broad spectrum of themes presented at the event. Of particular interest are the articles by F. Bonahon, "Geodesic Laminations on Surfaces", and D. Gabai, "Three Lectures on Foliations and Laminations on 3-manifolds", which are based on minicourses that took place during the conference.

Author : D. M. Gallo,R. M. Porter
Publisher : Unknown
Page : 132 pages
File Size : 51,5 Mb
Release : 2014-01-15
Category : Electronic
ISBN : 3662206757

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Kleinian Groups and Related Topics by D. M. Gallo,R. M. Porter Pdf

Author : Hernán González-Aguilar,Edgardo Ugalde
Publisher : Springer
Page : 223 pages
File Size : 41,6 Mb
Release : 2015-03-09
Category : Technology & Engineering
ISBN : 9783319098678

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Nonlinear Dynamics New Directions by Hernán González-Aguilar,Edgardo Ugalde Pdf

This book, along with its companion volume, Nonlinear Dynamics New Directions: Models and Applications, covers topics ranging from fractal analysis to very specific applications of the theory of dynamical systems to biology. This first volume is devoted to fundamental aspects and includes a number of important new contributions as well as some review articles that emphasize new development prospects. The second volume contains mostly new applications of the theory of dynamical systems to both engineering and biology. The topics addressed in the two volumes include a rigorous treatment of fluctuations in dynamical systems, topics in fractal analysis, studies of the transient dynamics in biological networks, synchronization in lasers, and control of chaotic systems, among others. This book also: · Presents a rigorous treatment of fluctuations in dynamical systems and explores a range of topics in fractal analysis, among other fundamental topics · Features recent developments on large deviations for higher-dimensional maps, a study of measures resisting multifractal analysis and a overview of complex Kleninan groups · Includes thorough review of recent findings that emphasize new development prospects

Author : D. B. A. Epstein
Publisher : CUP Archive
Page : 340 pages
File Size : 46,5 Mb
Release : 1986
Category : Mathematics
ISBN : 0521339057

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Low-dimensional Topology and Kleinian Groups by D. B. A. Epstein Pdf

Volume 2 is divided into three parts: the first 'Surfaces' contains an article by Thurston on earthquakes and by Penner on traintracks. The second part is entitled 'Knots and 3-Manifolds' and the final part 'Kleinian Groups'.