The geometry of discrete groups

Alan F. Beardon

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.

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  • 1 Preliminary Material.- 2 Matrices.- 3 Mobius Transformations on ?n.- 4 Complex Mobius 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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書名 The geometry of discrete groups
著作者等 Beardon, Alan F.
シリーズ名 Graduate texts in mathematics
出版元 Springer
刊行年月 c1983
版表示 1st ed. 1983. Corr. 2nd printing 1995
ページ数 xii, 337 p.
大きさ 24 cm
ISBN 3540907882
NCID BA00502862
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言語 英語
出版国 アメリカ合衆国