Foundations Of Hyperbolic Manifolds

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Foundations of Hyperbolic Manifolds

John Ratcliffe
Foundations of Hyperbolic Manifolds Book PDF

Author : John Ratcliffe
Publisher : Springer Science & Business Media
Page : 761 pages
File Size : 44,9 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.

Foundations of Hyperbolic Manifolds

John G. Ratcliffe
Foundations of Hyperbolic Manifolds Book PDF

Author : John G. Ratcliffe
Publisher : Springer Nature
Page : 800 pages
File Size : 49,7 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.

Fundamentals of Hyperbolic Manifolds

R. D. Canary,A. Marden,D. B. A. Epstein
Fundamentals of Hyperbolic Manifolds Book PDF

Author : R. D. Canary,A. Marden,D. B. A. Epstein
Publisher : Cambridge University Press
Page : 356 pages
File Size : 53,7 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.

Foundations of Hyperbolic Manifolds

John Ratcliffe
Foundations of Hyperbolic Manifolds Book PDF

Author : John Ratcliffe
Publisher : Springer
Page : 0 pages
File Size : 50,8 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.

Fundamentals of Hyperbolic Manifolds

R. D. Canary,Albert Marden,D. B. A. Epstein
Fundamentals of Hyperbolic Manifolds Book PDF

Author : R. D. Canary,Albert Marden,D. B. A. Epstein
Publisher : Cambridge University Press
Page : 348 pages
File Size : 42,8 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.

Hyperbolic Manifolds and Discrete Groups

Michael Kapovich
Hyperbolic Manifolds and Discrete Groups Book PDF

Author : Michael Kapovich
Publisher : Springer Science & Business Media
Page : 470 pages
File Size : 44,9 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.

Hyperbolic Manifolds

Albert Marden
Hyperbolic Manifolds Book PDF

Author : Albert Marden
Publisher : Cambridge University Press
Page : 535 pages
File Size : 53,9 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.

The Arithmetic of Hyperbolic 3-Manifolds

Colin Maclachlan,Alan W. Reid
The Arithmetic of Hyperbolic 3 Manifolds Book PDF

Author : Colin Maclachlan,Alan W. Reid
Publisher : Springer Science & Business Media
Page : 472 pages
File Size : 40,7 Mb
Release : 2013-04-17
Category : Mathematics
ISBN : 9781475767209

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

Recently there has been considerable interest in developing techniques based on number theory to attack problems of 3-manifolds; Contains many examples and lots of problems; Brings together much of the existing literature of Kleinian groups in a clear and concise way; At present no such text exists

Fundamentals of Hyperbolic Geometry

Richard Douglas Canary,Albert Marden,D. B. A. Epstein
Fundamentals of Hyperbolic Geometry Book PDF

Author : Richard Douglas Canary,Albert Marden,D. B. A. Epstein
Publisher : Unknown
Page : 348 pages
File Size : 49,9 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.

Lectures on Hyperbolic Geometry

Riccardo Benedetti,Carlo Petronio
Lectures on Hyperbolic Geometry Book PDF

Author : Riccardo Benedetti,Carlo Petronio
Publisher : Springer Science & Business Media
Page : 343 pages
File Size : 52,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642581588

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Lectures on Hyperbolic Geometry by Riccardo Benedetti,Carlo Petronio Pdf

Focussing on the geometry of hyperbolic manifolds, the aim here is to provide an exposition of some fundamental results, while being as self-contained, complete, detailed and unified as possible. Following some classical material on the hyperbolic space and the Teichmüller space, the book centers on the two fundamental results: Mostow's rigidity theorem (including a complete proof, following Gromov and Thurston) and Margulis' lemma. These then form the basis for studying Chabauty and geometric topology; a unified exposition is given of Wang's theorem and the Jorgensen-Thurston theory; and much space is devoted to the 3D case: a complete and elementary proof of the hyperbolic surgery theorem, based on the representation of three manifolds as glued ideal tetrahedra.

Hyperbolic Manifolds and Holomorphic Mappings

Shoshichi Kobayashi
Hyperbolic Manifolds and Holomorphic Mappings Book PDF

Author : Shoshichi Kobayashi
Publisher : World Scientific Publishing Company
Page : 160 pages
File Size : 48,6 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.

Outer Circles

A. Marden
Outer Circles Book PDF

Author : A. Marden
Publisher : Cambridge University Press
Page : 393 pages
File Size : 46,5 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.

A Gyrovector Space Approach to Hyperbolic Geometry

Abraham Ungar
A Gyrovector Space Approach to Hyperbolic Geometry Book PDF

Author : Abraham Ungar
Publisher : Springer Nature
Page : 182 pages
File Size : 51,7 Mb
Release : 2022-06-01
Category : Mathematics
ISBN : 9783031023965

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A Gyrovector Space Approach to Hyperbolic Geometry by Abraham Ungar Pdf

The mere mention of hyperbolic geometry is enough to strike fear in the heart of the undergraduate mathematics and physics student. Some regard themselves as excluded from the profound insights of hyperbolic geometry so that this enormous portion of human achievement is a closed door to them. The mission of this book is to open that door by making the hyperbolic geometry of Bolyai and Lobachevsky, as well as the special relativity theory of Einstein that it regulates, accessible to a wider audience in terms of novel analogies that the modern and unknown share with the classical and familiar. These novel analogies that this book captures stem from Thomas gyration, which is the mathematical abstraction of the relativistic effect known as Thomas precession. Remarkably, the mere introduction of Thomas gyration turns Euclidean geometry into hyperbolic geometry, and reveals mystique analogies that the two geometries share. Accordingly, Thomas gyration gives rise to the prefix "gyro" that is extensively used in the gyrolanguage of this book, giving rise to terms like gyrocommutative and gyroassociative binary operations in gyrogroups, and gyrovectors in gyrovector spaces. Of particular importance is the introduction of gyrovectors into hyperbolic geometry, where they are equivalence classes that add according to the gyroparallelogram law in full analogy with vectors, which are equivalence classes that add according to the parallelogram law. A gyroparallelogram, in turn, is a gyroquadrilateral the two gyrodiagonals of which intersect at their gyromidpoints in full analogy with a parallelogram, which is a quadrilateral the two diagonals of which intersect at their midpoints. Table of Contents: Gyrogroups / Gyrocommutative Gyrogroups / Gyrovector Spaces / Gyrotrigonometry

Hyperbolic Knot Theory

Jessica S. Purcell
Hyperbolic Knot Theory Book PDF

Author : Jessica S. Purcell
Publisher : American Mathematical Soc.
Page : 369 pages
File Size : 47,9 Mb
Release : 2020-10-06
Category : Education
ISBN : 9781470454999

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Hyperbolic Knot Theory by Jessica S. Purcell Pdf

This book provides an introduction to hyperbolic geometry in dimension three, with motivation and applications arising from knot theory. Hyperbolic geometry was first used as a tool to study knots by Riley and then Thurston in the 1970s. By the 1980s, combining work of Mostow and Prasad with Gordon and Luecke, it was known that a hyperbolic structure on a knot complement in the 3-sphere gives a complete knot invariant. However, it remains a difficult problem to relate the hyperbolic geometry of a knot to other invariants arising from knot theory. In particular, it is difficult to determine hyperbolic geometric information from a knot diagram, which is classically used to describe a knot. This textbook provides background on these problems, and tools to determine hyperbolic information on knots. It also includes results and state-of-the art techniques on hyperbolic geometry and knot theory to date. The book was written to be interactive, with many examples and exercises. Some important results are left to guided exercises. The level is appropriate for graduate students with a basic background in algebraic topology, particularly fundamental groups and covering spaces. Some experience with some differential topology and Riemannian geometry will also be helpful.

Accelerating Expansion

Gordon Belot
Accelerating Expansion Book PDF

Author : Gordon Belot
Publisher : Oxford University Press
Page : 241 pages
File Size : 50,8 Mb
Release : 2023-08-24
Category : Mathematics
ISBN : 9780192866462

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Accelerating Expansion by Gordon Belot Pdf

Accelerating Expansion explores some of the philosophical implications of modern cosmology, focused on the significance that the discovery of the accelerating expansion of the Universe has for our understanding of time, geometry, and physics. The appearance of the cosmological constant in the equations of general relativity allows one to model universes in which space has an inherent tendency towards expansion. This constant, introduced by Einstein but subsequently abandoned by him, returned to centre stage with the discovery of the accelerating expansion. This pedagogically-oriented essay begins with a study of the most basic and elegant relativistic world that involves a positive cosmological constant, de Sitter spacetime. It then turns to the relatives of de Sitter spacetime that dominate modern relativistic cosmology. Some of the topics considered include: the nature of time and simultaneity in de Sitter worlds; the sense in which de Sitter spacetime is a powerful dynamical attractor; the limited extent to which observation can give us information about the topology of space in a world undergoing accelerated expansion; and cosmologists' favourite sceptical worry about the reliability of evidence and the possibility of knowledge, the problem of Boltzmann brains.