Discontinuous Groups of Isometries in the Hyperbolic Plane

Discontinuous Groups of Isometries in the Hyperbolic Plane
Author :
Publisher : Walter de Gruyter
Total Pages : 389
Release :
ISBN-10 : 9783110891355
ISBN-13 : 3110891352
Rating : 4/5 (55 Downloads)

Book Synopsis Discontinuous Groups of Isometries in the Hyperbolic Plane by : Werner Fenchel

Download or read book Discontinuous Groups of Isometries in the Hyperbolic Plane written by Werner Fenchel and published by Walter de Gruyter. This book was released on 2011-05-12 with total page 389 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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). The current book is based on what became known as the famous Fenchel-Nielsen manuscript. Jakob Nielsen (1890-1959) started this project well before World War II, and his interest arose through his deep investigations on the topology of Riemann surfaces and from the fact that the fundamental group of a surface of genus greater than one is represented by such a discontinuous group. Werner Fenchel (1905-1988) joined the project later and overtook much of the preparation of the manuscript. The present book is special because of its very complete treatment of groups containing reversions and because it avoids the use of matrices to represent Moebius maps. This text is intended for students and researchers in the many areas of mathematics that involve the use of discontinuous groups.


Discontinuous Groups of Isometries in the Hyperbolic Plane Related Books

Discontinuous Groups of Isometries in the Hyperbolic Plane
Language: en
Pages: 389
Authors: Werner Fenchel
Categories: Mathematics
Type: BOOK - Published: 2011-05-12 - Publisher: Walter de Gruyter

DOWNLOAD EBOOK

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 t
Foundations of Hyperbolic Manifolds
Language: en
Pages: 761
Authors: John Ratcliffe
Categories: Mathematics
Type: BOOK - Published: 2013-03-09 - Publisher: Springer Science & Business Media

DOWNLOAD EBOOK

This book is an exposition of the theoretical foundations of hyperbolic manifolds. It is intended to be used both as a textbook and as a reference. Particular e
The Geometry of Discrete Groups
Language: en
Pages: 350
Authors: Alan F. Beardon
Categories: Mathematics
Type: BOOK - Published: 2012-12-06 - Publisher: Springer Science & Business Media

DOWNLOAD EBOOK

This text is intended to serve as an introduction to the geometry of the action of discrete groups of Mobius transformations. The subject matter has now been st
Generators and Relations in Groups and Geometries
Language: en
Pages: 455
Authors: A. Barlotti
Categories: Mathematics
Type: BOOK - Published: 2012-12-06 - Publisher: Springer Science & Business Media

DOWNLOAD EBOOK

Every group is represented in many ways as an epimorphic image of a free group. It seems therefore futile to search for methods involving generators and relatio
Algebraic Generalizations of Discrete Groups
Language: en
Pages: 338
Authors: Benjamin Fine
Categories: Mathematics
Type: BOOK - Published: 1999-07-27 - Publisher: CRC Press

DOWNLOAD EBOOK

A survey of one-relator products of cyclics or groups with a single defining relation, extending the algebraic study of Fuchsian groups to the more general cont