product iamge

Discontinuous Groups of Isometries in the Hyperbolic Plane

This document was uploaded by one of our users. The uploader already confirmed that they had the permission to publish it. If you are author/publisher or own the copyright of this documents, please report to us by using this DMCA report form.

Download
Search on Amazon

Simply click on the Download Book button.

Yes, Book downloads on Ebookily are 100% Free.

Sometimes the book is free on Amazon As well, so go ahead and hit "Search on Amazon"

"This is an introductory textbook on isometry groups of the hyperbolic plane. Interest in such groups dates back more than 120 years. - Examples appear in number theory (modular groups and triangle groups), the theory of elliptic functions, and the theory of linear differential equations in the complex domain (giving rise to the alternative name Fuchsian groups.). - "It is intended for students and researchers in the many areas of mathematics that involve the use of discontinuous groups."--Jacket.

Author(s): Werner Fenchel; Jakob Nielsen
Series: De Gruyter Studies in Mathematics, 29
Publisher: Walter de Gruyter
Year: 2003

Language: English
Pages: 364

Contents
Chapter I. Möbius Transformations and Non-Euclidean Geometry.
§1 Pencils of Circles - Inversive Geometry
§2 Cross-ratio
§3 Möbius Transformations, Direct and Reversed
§4 Invariant Points and Classification of Möbius Transformations
§5 Complex Distance of Two Pairs of Points
§6 Non-euclidean Metric
§7 Isometric transformations
§8 Non-euclidean trigonometry
§9 Products and Commutators of Motions
Chapter II. Discontinuous Groups of Motions and Reversions.
§10 the Concept of Discontinuity
§11 Groups with Invariant Points or Lines
§12 A Discontinuity Theorem
§13 ℱ-groups. Fundamental Set and Limit Set
§14 the Convex Domain of an ℱ-group. Characteristic and Isometric Neighbourhood
§15 Quasi-compactness Modulo ℱ and Finite Generation of ℱ
Chapter III. Surfaces Associated with Discontinuous Groups.
§16 the Surfaces D Modulo ℭ and K(ℱ) Modulo ℱ
§17 Area and Type Numbers
Chapter IV. Decompositions of Groups.
§18 Composition of Groups
§19 Decomposition of Groups
§20 Decompositions of ℱ-groups Containing Reflections
§21 Elementary Groups and Elementary Surfaces
§22 Complete Decomposition and Normal Form in the Case of Quasi-compactness
§23 Exhaustion in the Case of Non-quasi-compactness
Chapter V. Isomorphism and Homeomorphism.
§24 Topological and Geometrical Isomorphism
§25 Topological and Geometrical Homeomorphism
§26 Construction of G-mappings. Metric Parameters. Congruent Groups
Symbols and Definitions
Alphabets
Bibliography
Index