Foundations of Hyperbolic Manifolds: 149 (Graduate Texts in Mathematics, 149) - Softcover
Book 75 of 180: Graduate Texts in Mathematics
Synopsis
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. This book has been heavily class-tested and each chapter contains exercises and a section of historical remarks.
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From the Back Cover
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.
The book is divided into three parts. The first part is concerned with hyperbolic geometry and discrete groups. The main results are the characterization of hyperbolic reflection groups and Euclidean crystallographic groups. The second part is devoted to the theory of hyperbolic manifolds. The main results are Mostow's rigidity theorem and the determination of the global geometry of hyperbolic manifolds of finite volume. The third part integrates the first two parts in a development of the theory of hyperbolic orbifolds. The main result is Poincare«s fundamental polyhedron theorem.
The exposition if at the level of a second year graduate student with particular emphasis placed on readability and completeness of argument. After reading this book, the reader will have the necessary background to study the current research on hyperbolic manifolds.
The second edition is a thorough revision of the first edition that embodies hundreds of changes, corrections, and additions, including over sixty new lemmas, theorems, and corollaries. The new main results are Schl\¬afli's differential formula and the $n$-dimensional Gauss-Bonnet theorem.
John G. Ratcliffe is a Professor of Mathematics at Vanderbilt University.
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Foundations of Hyperbolic Manifolds
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Taschenbuch. Condition: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -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. 796 pp. Englisch. Seller Inventory # 9781441922021
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Taschenbuch. Condition: Neu. Foundations of Hyperbolic Manifolds | John Ratcliffe | Taschenbuch | Englisch | Springer | EAN 9781441922021 | Verantwortliche Person für die EU: Springer Nature Customer Service Center GmbH, Europaplatz 3, 69115 Heidelberg, productsafety[at]springernature[dot]com | Anbieter: preigu. Seller Inventory # 107207945
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Foundations of Hyperbolic Manifolds
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Taschenbuch. Condition: Neu. Druck auf Anfrage Neuware - Printed after ordering - 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. The reader is assumed to have a basic knowledge of algebra and topology at the first year graduate level of an American university. 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. The second edition contains hundreds of changes, corrections and new additions include. The exercises have been thoroughly reworked and over 100 new exercises have been added. The author has also prepared a solutions manual which is available to professors who choose to adopt this text for their course. This carefully written textbook has been heavily class-tested and each chapter contains exercises and a section of historical remarks. Seller Inventory # 9781441922021