Overview

This text is about the geometric theory of discrete groups and the associated tesselations of the underlying space. The theory of Mobius transformations in n-dimensional Euclidean space is developed. These transformations are discussed as isometries of hyperbolic space and are then identified with the elementary transformations of complex analysis. A detailed account of analytic hyperbolic trigonometry is given, and this forms the basis of the subsequent analysis of tesselations of the hyperbolic plane. Emphasis is placed on the geometrical aspects of the subject and on the universal constraints which must be satisfied by all tesselations.

Full Product Details

Author:   Alan F. Beardon
Publisher:   Springer-Verlag New York Inc.
Imprint:   Springer-Verlag New York Inc.
Edition:   1st ed. 1983. Corr. 2nd printing 1995
Volume:   91
Dimensions:   Width: 15.50cm , Height: 2.00cm , Length: 23.50cm
Weight:   1.490kg
ISBN:  

9780387907888

ISBN 10:   0387907882
Pages:   340
Publication Date:   09 May 1983
Audience:   College/higher education ,  Professional and scholarly ,  Undergraduate ,  Postgraduate, Research & Scholarly
Format:   Hardback
Publisher's Status:   Active
Availability:   In Print  
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Table of Contents

1 Preliminary Material.- 2 Matrices.- 3 Möbius Transformations on ?n.- 4 Complex Möbius Transformations.- 5 Discontinuous Groups.- 6 Riemann Surfaces.- 7 Hyperbolic Geometry.- 8 Fuchsian Groups.- 9 Fundamental Domains.- 10 Finitely Generated Groups.- 11 Universal Constraints on Fuchsian Groups.- References.

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