The geometry of discrete groups / Alan F. Beardon.

Format:

Book

Author/Creator:

Beardon, Alan F.

Series:

Graduate texts in mathematics ; 91.

Graduate texts in mathematics ; 91

Language:

English

Subjects (All):

Discrete groups.

Isometrics (Mathematics).

Möbius transformations.

Geometry, Hyperbolic.

Physical Description:

xii, 337 pages : illustrations ; 24 cm.

Place of Publication:

New York : Springer-Verlag, [1983]

Summary:

This text is about the geometric theory of discrete groups and the associated tesselations of the underlying space. The theory of MC6bius 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.

Notes:

Includes bibliographical references and index.

OCLC:

8931052