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Geometry of Discrete Groups

Geometry of Discrete Groups - 95 edition

ISBN13: 978-0387907888

Cover of Geometry of Discrete Groups 95 (ISBN 978-0387907888)
ISBN13: 978-0387907888
ISBN10: 0387907882 Edition: 95
Copyright: 1995
Publisher: Springer-Verlag New York
Published: 1995
International: No

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Geometry of Discrete Groups - 95 edition

ISBN13: 978-0387907888

Alan F. Beardon

ISBN13: 978-0387907888
ISBN10: 0387907882 Edition: 95
Copyright: 1995
Publisher: Springer-Verlag New York
Published: 1995
International: No
Summary

This text is about the geometric theory of discrete groups and the associated tesselations of the underlying space. The theory of M ’ bius 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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