Foundations of Hyperbolic Manifolds [Hardcover]

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.

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.

Euclidean Geometry.- Spherical Geometry.- Hyperbolic Geometry.- Inversive Geometry.- Isometries of Hyperbolic Space.- Geometry of Discrete Groups.- Classical Discrete Groups.- Geometric Manifolds.- Geometric Surfaces.- Hyperbolic 3-Manifolds.- Hyperbolic n-Manifolds.- Geometrically Finite n-Manifolds.- Geometric Orbifolds.

From the reviews of the second edition:

Designed to be useful as both textbook and a reference, this book renders a real service to the mathematical community by putting together the tools and prerequisites needed to enter the territory of Thurstons formidable theory of hyperbolic 3-mainfolds & . Every chapter is followed by historical notes, with attributions to the relevant literature, both of the originators of the idea present in the chapter and of modern presentation thereof. The bibliography contains 463 entries. (Victor V. Pambuccian, Zentralblatt MATH, Vol. 1106 (8), 2007)

This book is an exposition of the theoretical foundations of hyperbolic manifolds. It is intended to be used bol3|