The Geometry of Discrete Groups

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

שנה

2012

שפה

English

הוצאה

Springer New York

מהדורות

4

עמודים

340

ISBN

9781461270225

מקור הנתונים: Wikidata