Quilts: Central Extensions, Braid Actions, and Finite Groups
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 re
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1731
Lecture Notes in Mathematics Editors: A. Dold, Heidelberg F. Takens, Groningen B. Teissier, Paris
1731
Springer Berlin Heidelberg New York Barcelona Hong Kong London Milan Paris Singapore Tokyo
TimHsu
Quilts: Central Extensions, Braid Actions, and Finite Groups
Springer
Author Tim Hsu Department of Mathematics Pomona College 61ON. College Ave. Claremont CA 91711-6348, USA E-mail: [email protected]
Cataloging-in-Publication Data applied for Die Deutsche Bibliothek - CIP-Einheitsaufnahme Hsu, Tim: Quilts: central extensions, braid actions, and finite groups I Tim Hsu. - Berlin; Heidelberg; New York; Barcelona; Hong Kong; London ; Milan; Paris; Singapore; Tokyo: Springer, 2000 (Lecture notes in mathematics ; 1731) ISBN 3-540-67397-0
Mathematics Subject Classification (2000): 20D08, 20E22, 20F36, 20HI0 ISSN 0075-8434 ISBN 3-540-67397-0 Springer-Verlag Berlin Heidelberg New York This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, re-use of illustrations, recitation, broadcasting, reproduction on microfilms or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer-Verlag. Violations are liable for prosecution under the German Copyright Law. Springer-Verlag is a company in the BertelsmannSpringer publishing group. © Springer-Verlag Berlin Heidelberg 2000 Printed in Germany The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. Typesetting: Camera-ready TEX output by the author Printed on acid-free paper SPIN: 10724981 4113143/du
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Preface
Quilts, as developed by Norton, Parker, Conway, and the author, are 2complexes used to analyze actions and subgroups of the 3string braid group, or more generally, to analyze actions and subgroups of certain central extensions of triangle groups. This monograph describes the fundamentals of quilt theory, including basic definitions, main results, and applications to central extensions, braid actions, and finite groups. Though the monograph contains some purely expository material, it is primarily a research monograph. Indeed, most of the results have not previously been published in a widely available form, and many results appear here in print for the first time. The material in this monograph should be accessible to graduate students. More specifically, the only background necessary is a first graduate course in algebra, though some knowledge of algebraic topology and familiarity with finite group theory is helpful. The methods and results may be relevant to researchers interested in finite groups, moonshine, central ex
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