Foundations of Hyperbolic Manifolds

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Springer Science & Business Media, 23.08.2006 - 782 Seiten

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.

 

Inhalt

Euclidean Geometry
1
Spherical Geometry
35
Hyperbolic Geometry
54
Inversive Geometry
100
Isometries of Hyperbolic Space
144
Geometry of Discrete Groups
188
Classical Discrete Groups
263
Geometric Manifolds
334
Geometric Surfaces
375
Hyperbolic 3Manifolds
435
Hyperbolic nManifolds
508
Geometrically Finite nManifolds
600
Geometric Orbifolds
681
Bibliography
745
Index
768
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