Quilts are 2-complexes used to analyze actions and subgroups of the 3-string braid group and similar groups. This monograph establishes the fundamentals of quilts and discusses connections with central extensions, braid actions, and finite groups. Most results have not previously appeared in a widely available form, and many results appear in print for the first time. This monograph is accessible to graduate students, as a substantial amount of background material is included. The methods and results may be relevant to researchers interested in infinite groups, moonshine, central extensions, triangle groups, dessins d'enfants, and monodromy actions of braid groups.
Author(s): Tim Hsu
Series: Lecture Notes in Mathematics
Edition: 1
Publisher: Springer
Year: 2000
Language: English
Pages: 188
1731 Tim Hsu......Page 1
Quilts: Central Extensions, Braid Actions, and Finite Groups......Page 3
Preface......Page 5
Contents......Page 6
1. Introduction......Page 12
2. Background material......Page 20
3. Quilts......Page 39
4. Norton systems and their quilts......Page 64
5. Examples of quilts......Page 80
6. The combinatorics of quilts......Page 89
7. Classical interpretations of quilts......Page 100
8. Presentations and the structure problem......Page 107
9. Small snug quilts......Page 124
10. Monodromy systems......Page 131
11. Quilts for groups involved in the Monster......Page 136
12. Some results on the structure problem......Page 153
13. Further directions......Page 159
A. Independent generators for modular subgroups......Page 167
References......Page 181
Index......Page 185
