Foundations of Hyperbolic Manifolds. 3rd ed. 2019

種類:

電子ブック

責任表示:

by John G. Ratcliffe

出版情報:

Cham : Springer International Publishing : Imprint: Springer, 2019

著者名:

• Ratcliffe, John G.
• SpringerLink (Online service)

シリーズ名:

Graduate Texts in Mathematics ; 149

ISBN:

9783030315979 [3030315975]    

注記:

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.
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 third edition greatly expands upon the second with an abundance of additional content, including a section dedicated to arithmetic hyperbolic groups. Over 40 new lemmas, theorems, and corollaries feature, along with more than 70 additional exercises. Color adds a new dimension to figures throughout. 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 Poincaré’s fundamental p

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