基本説明
Intended to be used both as a textbook and as a reference. The second edition contains hundreds of changes and include: A more thorough discussion of polytopes; Discussion of Simplex Reflection groups has been expanded to give a complete classification of the Gram matrices of spherical, Euclidean and hyperbolic n-simplices; and more.
Full Description
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.
Contents
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.
