Ratcliffe Foundations of Hyperbolic Manifolds

Erscheinungsjahr 2013
ISBN: 978-1-4757-4013-4
Verlag: Springer US
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, Band 149, 750 Seiten, eBook

Reihe: Graduate Texts in Mathematics

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.

Zielgruppe

Graduate

Autoren/Hrsg.

Ratcliffe, John

Inhaltsverzeichnis

1 Euclidean Geometry.- 2 Spherical Geometry.- 3 Hyperbolic Geometry.- 4 Inversive Geometry.- 5 Isometries of Hyperbolic Space.- 6 Geometry of Discrete Groups.- 7 Classical Discrete Groups.- 8 Geometric Manifolds.- 9 Geometric Surfaces.- 10 Hyperbolic 3-Manifolds.- 11 Hyperbolic n-Manifolds.- 12 Geometrically Finite n-Manifolds.- 13 Geometric Orbifolds.