Fundamentals Of Hyperbolic Manifolds

Author : R. D. Canary,A. Marden,D. B. A. Epstein
Publisher : Cambridge University Press
Page : 356 pages
File Size : 45,8 Mb
Release : 2006-04-13
Category : Mathematics
ISBN : 113944719X

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Fundamentals of Hyperbolic Manifolds by R. D. Canary,A. Marden,D. B. A. Epstein Pdf

Presents reissued articles from two classic sources on hyperbolic manifolds. Part I is an exposition of Chapters 8 and 9 of Thurston's pioneering Princeton Notes; there is a new introduction describing recent advances, with an up-to-date bibliography, giving a contemporary context in which the work can be set. Part II expounds the theory of convex hull boundaries and their bending laminations. A new appendix describes recent work. Part III is Thurston's famous paper that presents the notion of earthquakes in hyperbolic geometry and proves the earthquake theorem. The final part introduces the theory of measures on the limit set, drawing attention to related ergodic theory and the exponent of convergence. The book will be welcomed by graduate students and professional mathematicians who want a rigorous introduction to some basic tools essential for the modern theory of hyperbolic manifolds.

Author : John Ratcliffe
Publisher : Springer Science & Business Media
Page : 761 pages
File Size : 47,8 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9781475740134

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Foundations of Hyperbolic Manifolds by John Ratcliffe Pdf

This book is an exposition of the theoretical foundations of hyperbolic manifolds. It is intended to be used both as a textbook and as a reference. Particular emphasis has been placed on readability and completeness of ar gument. The treatment of the material is for the most part elementary and self-contained. The reader is assumed to have a basic knowledge of algebra and topology at the first-year graduate level of an American university. The book is divided into three parts. The first part, consisting of Chap ters 1-7, is concerned with hyperbolic geometry and basic properties of discrete groups of isometries of hyperbolic space. The main results are the existence theorem for discrete reflection groups, the Bieberbach theorems, and Selberg's lemma. The second part, consisting of Chapters 8-12, is de voted to the theory of hyperbolic manifolds. The main results are Mostow's rigidity theorem and the determination of the structure of geometrically finite hyperbolic manifolds. The third part, consisting of Chapter 13, in tegrates the first two parts in a development of the theory of hyperbolic orbifolds. The main results are the construction of the universal orbifold covering space and Poincare's fundamental polyhedron theorem.

Author : Richard Douglas Canary,Albert Marden,D. B. A. Epstein
Publisher : Unknown
Page : 348 pages
File Size : 43,8 Mb
Release : 2014-05-14
Category : Geometry, Hyperbolic
ISBN : 1139126938

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Fundamentals of Hyperbolic Geometry by Richard Douglas Canary,Albert Marden,D. B. A. Epstein Pdf

Reissued articles from two classic sources on hyperbolic manifolds with new sections describing recent work.

Author : John G. Ratcliffe
Publisher : Springer Nature
Page : 800 pages
File Size : 51,8 Mb
Release : 2019-10-23
Category : Mathematics
ISBN : 9783030315979

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Foundations of Hyperbolic Manifolds by John G. Ratcliffe Pdf

This heavily class-tested book is an exposition of the theoretical foundations of hyperbolic manifolds. It is a both a textbook and a reference. A basic knowledge of algebra and topology at the first year graduate level of an American university is assumed. The first part is concerned with hyperbolic geometry and discrete groups. The second part is devoted to the theory of hyperbolic manifolds. The third part integrates the first two parts in a development of the theory of hyperbolic orbifolds. Each chapter contains exercises and a section of historical remarks. A solutions manual is available separately.

Author : R. D. Canary,Albert Marden,D. B. A. Epstein
Publisher : Cambridge University Press
Page : 348 pages
File Size : 52,8 Mb
Release : 2006-04-13
Category : Mathematics
ISBN : 9780521615587

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Fundamentals of Hyperbolic Manifolds by R. D. Canary,Albert Marden,D. B. A. Epstein Pdf

Presents reissued articles from two classic sources on hyperbolic manifolds. Part I is an exposition of Chapters 8 and 9 of Thurston's pioneering Princeton Notes; there is a new introduction describing recent advances, with an up-to-date bibliography, giving a contemporary context in which the work can be set. Part II expounds the theory of convex hull boundaries and their bending laminations. A new appendix describes recent work. Part III is Thurston's famous paper that presents the notion of earthquakes in hyperbolic geometry and proves the earthquake theorem. The final part introduces the theory of measures on the limit set, drawing attention to related ergodic theory and the exponent of convergence. The book will be welcomed by graduate students and professional mathematicians who want a rigorous introduction to some basic tools essential for the modern theory of hyperbolic manifolds.

Author : Michael Kapovich
Publisher : Springer Science & Business Media
Page : 470 pages
File Size : 44,7 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 : Katsuhiko Matsuzaki,Masahiko Taniguchi
Publisher : Clarendon Press
Page : 265 pages
File Size : 48,9 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 : Albert Marden
Publisher : Cambridge University Press
Page : 535 pages
File Size : 42,5 Mb
Release : 2016-02
Category : Mathematics
ISBN : 9781107116740

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Hyperbolic Manifolds by Albert Marden Pdf

This study of hyperbolic geometry has both pedagogy and research in mind, and includes exercises and further reading for each chapter.

Author : John Ratcliffe
Publisher : Springer
Page : 0 pages
File Size : 55,8 Mb
Release : 2008-11-01
Category : Mathematics
ISBN : 0387512969

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Foundations of Hyperbolic Manifolds by John Ratcliffe Pdf

This heavily class-tested book is an exposition of the theoretical foundations of hyperbolic manifolds. It is a both a textbook and a reference. A basic knowledge of algebra and topology at the first year graduate level of an American university is assumed. The first part is concerned with hyperbolic geometry and discrete groups. The second part is devoted to the theory of hyperbolic manifolds. The third part integrates the first two parts in a development of the theory of hyperbolic orbifolds. Each chapter contains exercises and a section of historical remarks. A solutions manual is available separately.

Author : Colin MacLachlan,Alan W. Reid
Publisher : Unknown
Page : 484 pages
File Size : 51,9 Mb
Release : 2014-01-15
Category : Electronic
ISBN : 1475767218

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The Arithmetic of Hyperbolic 3-Manifolds by Colin MacLachlan,Alan W. Reid Pdf

Author : A. Marden
Publisher : Cambridge University Press
Page : 393 pages
File Size : 41,6 Mb
Release : 2007-05-31
Category : Mathematics
ISBN : 9781139463768

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Outer Circles by A. Marden Pdf

We live in a three-dimensional space; what sort of space is it? Can we build it from simple geometric objects? The answers to such questions have been found in the last 30 years, and Outer Circles describes the basic mathematics needed for those answers as well as making clear the grand design of the subject of hyperbolic manifolds as a whole. The purpose of Outer Circles is to provide an account of the contemporary theory, accessible to those with minimal formal background in topology, hyperbolic geometry, and complex analysis. The text explains what is needed, and provides the expertise to use the primary tools to arrive at a thorough understanding of the big picture. This picture is further filled out by numerous exercises and expositions at the ends of the chapters and is complemented by a profusion of high quality illustrations. There is an extensive bibliography for further study.

Author : Shoshichi Kobayashi
Publisher : World Scientific Publishing Company
Page : 160 pages
File Size : 50,9 Mb
Release : 2005-11-02
Category : Mathematics
ISBN : 9789813101937

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Hyperbolic Manifolds and Holomorphic Mappings by Shoshichi Kobayashi Pdf

The first edition of this influential book, published in 1970, opened up a completely new field of invariant metrics and hyperbolic manifolds. The large number of papers on the topics covered by the book written since its appearance led Mathematical Reviews to create two new subsections “invariant metrics and pseudo-distances” and “hyperbolic complex manifolds” within the section “holomorphic mappings”. The invariant distance introduced in the first edition is now called the “Kobayashi distance”, and the hyperbolicity in the sense of this book is called the “Kobayashi hyperbolicity” to distinguish it from other hyperbolicities. This book continues to serve as the best introduction to hyperbolic complex analysis and geometry and is easily accessible to students since very little is assumed. The new edition adds comments on the most recent developments in the field.

Author : Jean-Pierre Otal
Publisher : American Mathematical Soc.
Page : 150 pages
File Size : 51,5 Mb
Release : 2001
Category : Mathematics
ISBN : 0821821539

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The Hyperbolization Theorem for Fibered 3-Manifolds by Jean-Pierre Otal Pdf

For graduate students familiar with low-dimensional topology and researchers in geometry and topology, Otal (CNRS-UMR 128, Lyon) offers a complete proof of Thurston's hyperbolization theorem for 3-manifolds that fiber as surface bundles. The original Le Theoreme d'Hyperbolisation pour les Varietes de Dimension 3, published by the French Mathematical Society in 1996, has been translated by Leslie D. Kay. c. Book News Inc.

Author : Serge Lang
Publisher : Springer Science & Business Media
Page : 553 pages
File Size : 51,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461205418

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Fundamentals of Differential Geometry by Serge Lang Pdf

This book provides an introduction to the basic concepts in differential topology, differential geometry, and differential equations, and some of the main basic theorems in all three areas. This new edition includes new chapters, sections, examples, and exercises. From the reviews: "There are many books on the fundamentals of differential geometry, but this one is quite exceptional; this is not surprising for those who know Serge Lang's books." --EMS NEWSLETTER

Author : Albert Marden
Publisher : Unknown
Page : 427 pages
File Size : 47,9 Mb
Release : 2007
Category : Three-manifolds (Topology)
ISBN : 0511322186

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Outer Circles by Albert Marden Pdf

Excellent introductory text on the contemporary theory of hyperbolic 3-manifolds.