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Fuchsian Groups : Chicago Lectures in Mathematics - Svetlana Katok

Fuchsian Groups

Chicago Lectures in Mathematics

Paperback

Published: 1st January 1992
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This introductory text provides a thoroughly modern treatment of Fuchsian groups that addresses both the classical material and recent developments in the field. A basic example of lattices in semisimple groups, Fuchsian groups have extensive connections to the theory of a single complex variable, number theory, algebraic and differential geometry, topology, Lie theory, representation theory, and group theory.

Preface
Hyperbolic geometry
The hyperbolic metric
Geodesics
Isometrics
Hyperbolic area and the Gauss-Bonnet formula
Hyperbolic trigonometry
Comparison between hyperbolic, spherical and Euclidean trigonometry Exercises for Chapter 1
Fuchsian groups
The group PSL(2,R)
Discrete and properly discontinuous groups
Algebraic properties of Fuchsian groups
Elementary groups Exercises for Chapter 2
Fundamental regions
Definition of a fundamental region
The Dirichlet region
Isometric circles and the Ford fundamental region
The limit set of [ ]3.5. Structure of a Dirichlet region
Connection with Riemann surfaces and homogeneous spaces Exercises for Chapter 3
Geometry of Fuchsian groups
Geometrically finite Fuchsian groups
Cocompact Fuchsian groups
The signature of a Fuchsian group
Fuchsian groups generated by reflections
Fuchsian groups of the first kind
Finitely generated Fuchsian groups Exercises for Chapter 4
Arithmetic Fuchsian groups
Definitions of arithmetic Fuchsian groups
Fuchsian groups derived from quaternion algebras
Criteria for arithmeticity
Compactness of [ ] for Fuchsian groups derived from division quaternion algebras
The modular group and its subgroups
Examples Exercises for Chapter 5 Hints for Selected Exercises
Bibliography
Index
Table of Contents provided by Publisher. All Rights Reserved.

ISBN: 9780226425832
ISBN-10: 0226425835
Series: Chicago Lectures in Mathematics
Audience: Professional
Format: Paperback
Language: English
Number Of Pages: 186
Published: 1st January 1992
Publisher: The University of Chicago Press
Country of Publication: US
Dimensions (cm): 20.6 x 13.5  x 1.27
Weight (kg): 0.23