Foundations Of Hyperbolic Manifolds
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Foundations Of Hyperbolic Manifolds
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Author : John Ratcliffe
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-08-23
Foundations Of Hyperbolic Manifolds written by John Ratcliffe and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-08-23 with Mathematics categories.
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.
Foundations Of Hyperbolic Manifolds
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Author : John Ratcliffe
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
Foundations Of Hyperbolic Manifolds written by John Ratcliffe and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-09 with Mathematics categories.
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
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Author : John G. Ratcliffe
language : en
Publisher: Springer Nature
Release Date : 2019-10-23
Foundations Of Hyperbolic Manifolds written by John G. Ratcliffe and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-10-23 with Mathematics categories.
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.
Foundations Of Hyperbolic Manifolds
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Author : John Ratcliffe
language : en
Publisher:
Release Date : 2014-01-15
Foundations Of Hyperbolic Manifolds written by John Ratcliffe and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-15 with categories.
Fundamentals Of Hyperbolic Manifolds
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Author : R. D. Canary
language : en
Publisher: Cambridge University Press
Release Date : 2006-04-13
Fundamentals Of Hyperbolic Manifolds written by R. D. Canary and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-04-13 with Mathematics categories.
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
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Author : John Ratcliffe
language : en
Publisher: Springer
Release Date : 2008-11-01
Foundations Of Hyperbolic Manifolds written by John Ratcliffe and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-11-01 with Mathematics categories.
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.
The Arithmetic Of Hyperbolic 3 Manifolds
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Author : Colin Maclachlan
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17
The Arithmetic Of Hyperbolic 3 Manifolds written by Colin Maclachlan and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-17 with Mathematics categories.
For the past 25 years, the Geometrization Program of Thurston has been a driving force for research in 3-manifold topology. This has inspired a surge of activity investigating hyperbolic 3-manifolds (and Kleinian groups), as these manifolds form the largest and least well- understood class of compact 3-manifolds. Familiar and new tools from diverse areas of mathematics have been utilized in these investigations, from topology, geometry, analysis, group theory, and from the point of view of this book, algebra and number theory. This book is aimed at readers already familiar with the basics of hyperbolic 3-manifolds or Kleinian groups, and it is intended to introduce them to the interesting connections with number theory and the tools that will be required to pursue them. While there are a number of texts which cover the topological, geometric and analytical aspects of hyperbolic 3-manifolds, this book is unique in that it deals exclusively with the arithmetic aspects, which are not covered in other texts. Colin Maclachlan is a Reader in the Department of Mathematical Sciences at the University of Aberdeen in Scotland where he has served since 1968. He is a former President of the Edinburgh Mathematical Society. Alan Reid is a Professor in the Department of Mathematics at The University of Texas at Austin. He is a former Royal Society University Research Fellow, Alfred P. Sloan Fellow and winner of the Sir Edmund Whittaker Prize from The Edinburgh Mathematical Society. Both authors have published extensively in the general area of discrete groups, hyperbolic manifolds and low-dimensional topology.
Lectures On Hyperbolic Geometry
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Author : Riccardo Benedetti
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Lectures On Hyperbolic Geometry written by Riccardo Benedetti and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
In recent years hyperbolic geometry has been the object and the preparation for extensive study that has produced important and often amazing results and also opened up new questions. The book concerns the geometry of manifolds and in particular hyperbolic manifolds; its aim is to provide an exposition of some fundamental results, and to be as far as possible self-contained, complete, detailed and unified. Since it starts from the basics and it reaches recent developments of the theory, the book is mainly addressed to graduate-level students approaching research, but it will also be a helpful and ready-to-use tool to the mature researcher. After collecting some classical material about the geometry of the hyperbolic space and the Teichmüller space, the book centers on the two fundamental results: Mostow's rigidity theorem (of which a complete proof is given following Gromov and Thurston) and Margulis' lemma. These results form the basis for the study of the space of the hyperbolic manifolds in all dimensions (Chabauty and geometric topology); a unified exposition is given of Wang's theorem and the Jorgensen-Thurston theory. A large part is devoted to the three-dimensional case: a complete and elementary proof of the hyperbolic surgery theorem is given based on the possibility of representing three manifolds as glued ideal tetrahedra. The last chapter deals with some related ideas and generalizations (bounded cohomology, flat fiber bundles, amenable groups). This is the first book to collect this material together from numerous scattered sources to give a detailed presentation at a unified level accessible to novice readers.
Hyperbolic Manifolds
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Author : Albert Marden
language : en
Publisher: Cambridge University Press
Release Date : 2016-02
Hyperbolic Manifolds written by Albert Marden and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-02 with Mathematics categories.
This study of hyperbolic geometry has both pedagogy and research in mind, and includes exercises and further reading for each chapter.
Foundations Of Hyperbolic Manifolds
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Author : John Ratcliffe
language : en
Publisher: Springer
Release Date : 2010-11-23
Foundations Of Hyperbolic Manifolds written by John Ratcliffe and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-11-23 with Mathematics categories.
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.