Foundations of hyperbolic manifolds
2 - 3 weken
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.
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.
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.
- 1 Bekijk alle specificaties
Taal: en
Bindwijze: Hardcover
Oorspronkelijke releasedatum: 23 augustus 2006
Aantal pagina's: 796
Illustraties: Nee
Hoofdauteur: John Ratcliffe
Tweede Auteur: John G. Ratcliffe
Hoofduitgeverij: Springer-Verlag New York Inc.
Originele titel: Foundations of Hyperbolic Manifolds
Editie: 2
Extra groot lettertype: Nee
Product breedte: 152 mm
Product hoogte: 41 mm
Product lengte: 234 mm
Studieboek: Ja
Verpakking breedte: 156 mm
Verpakking hoogte: 41 mm
Verpakking lengte: 235 mm
Verpakkingsgewicht: 2830 g
EAN: 9780387331973