Discontinous Groups of Isometries

Discontinous Groups of Isometries

by Werner Fenchel, Jakob Nielsen, Asmus L. Schmidt
     
 

ISBN-10: 3110175266

ISBN-13: 9783110175264

Pub. Date: 02/28/2003

Publisher: De Gruyter

Fuchsian groups play a central role in various important fields of mathematics. 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, Werner Fenchel

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Overview

Fuchsian groups play a central role in various important fields of mathematics. 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, Werner Fenchel (1905-1988) joined later and overtook the much of the preparation of the manuscript.

Professor Asmus Schmidt (University of Copenhagen) is the editor of this first publication in book form of the Fenchel-Nielsen notes. It is on his initiative that the long and difficult way of getting the original notes into the proper shape ready for publication succeeded.

Product Details

ISBN-13:
9783110175264
Publisher:
De Gruyter
Publication date:
02/28/2003
Series:
de Gruyter Studies in Mathematics Series, #29
Pages:
388
Product dimensions:
6.14(w) x 9.21(h) x 0.88(d)
Age Range:
18 Years

Table of Contents

Preface
Life and work of the Authors
IMobius transformations and non-euclidean geometry1
1Pencils of circles - inversive geometry1
2Cross-ratio4
3Mobius transformations, direct and reversed6
4Invariant points and classification of Mobius transformations8
5Complex distance of two pairs of points14
6Non-euclidean metric18
7Isometric transformations23
8Non-euclidean trigonometry27
9Products and commutators of motions43
IIDiscontinuous groups of motions and reversions58
10The concept of discontinuity58
11Groups with invariant points or lines70
12A discontinuity theorem78
13[actual symbol not reproducible]-groups. Fundamental set and limit set82
14The convex domain of an [actual symbol not reproducible]-group. Characteristic and isometric neighbourhood95
15Quasi-compactness modulo [actual symbol not reproducible] and finite generation of [actual symbol not reproducible]115
IIISurfaces associated with discontinuous groups127
16The surfaces [actual symbol not reproducible] module [actual symbol not reproducible] and K ([actual symbol not reproducible]) modulo [actual symbol not reproducible]127
17Area and type numbers135
IVDecompositions groups153
18Composition of groups153
19Decomposition of groups174
20Decompositions of [actual symbol not reproducible]-groups containing reflections196
21Elementary groups and elementary surfaces213
22Complete decomposition and normal form in the case of quasi-compactness242
23Exhaustion in the case of non-quasi-compactness270
VIsomorphism and homeomorphism283
24Topological and geometrical isomorphism283
25Topological and geometrical homeomorphism308
26Construction of g-mappings. Metric parameters. Congruent groups318
Symbols and definitions349
Alphabets353
Bibliography355
Index361

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