Fuchsian Groups

By: Svetlana Katok

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Paperback | 1 August 1992 | Edition Number 1

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186 Pages

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2.03 x 1.34 x 0.11

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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.

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You Can Find This Book In

Non-Fiction Mathematics Groups & Group Theory Calculus & Mathematical Analysis Algebra Business & Management Geometry Euclidean Geometry

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.

Fuchsian Groups

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Paperback

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