Quilts: Central Extensions, Braid Actions, and Finite Groups

2000
ISBN: 978-3-540-67397-2
Verlag: Springer Berlin Heidelberg

Buch, Englisch, Band 1731, 190 Seiten, Format (B × H): 155 mm x 233 mm, Gewicht: 312 g

Reihe: Lecture Notes in Mathematics

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.

Zielgruppe

Research

Autoren/Hrsg.

Hsu, Tim

Fachgebiete

• Mathematik | Informatik Mathematik Algebra Algebraische Strukturen, Gruppentheorie
• Mathematik | Informatik Mathematik Algebra Homologische Algebra

Inhaltsverzeichnis

Background material.- Quilts.- Norton systems and their quilts.- Examples of quilts.- The combinatorics of quilts.- Classical interpretations of quilts.- Presentations and the structure problem.- Small snug quilts.- Monodromy systems.- Quilts for groups involved in the monster.- Some results on the structure problem.- Further directions.