Non-Semisimple Topological Quantum Field Theories for 3-Manifolds with Corners
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Thomas Kerler Volodymyr V. Lyubashenko
Non-Semisimple Topological Quantum Field Theories for 3-Manifolds with Corners
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Authors Thomas Kerler Department of Mathematics The Ohio State University 231 West 18th Avenue Columbus, Ohio 43210, USA
Volodymyr V. Lyubashenko Institute of Mathematics National Academy of Sciences of Ukraine 3, Tereshchenkivska st. Kyiv-4, 01601 MSP, Ukraine
E-mail: [email protected]
E-mail: [email protected]
Cataloging-in-Publication Data applied for
Mathematics Subject Classification (2000): 16W30, 18D05, 18D10, 18E10, 57N10, 57N13, 57N70 Physics and Astronomy Classification (1999): 11.10.Cd, 11.10.Kk, 11.25.Hf, 11.25.Sq ISSN 0075-8434 ISBN 3-540-42416-4 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 Berlin Heidelberg New York a member of BertelsmannSpringer Science+Business Media GmbH http://www.springer.de © Springer-Verlag Berlin Heidelberg 2001 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 authors SPIN: 10847519
41/3142-543210 - Printed on acid-free paper
Contents
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0. 1
0.2 0.3 0.4
1.
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The Double
Category of Framed, Relative 3-Cobordisms Category of Surfaces with Boundaries
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4.
1.3
Consequences of the Double Category Picture Mapping Class Groups, Framed Braid Groups, and Balancing Some Facts about Handle Decompositions b -4 Obb The Central Extension 04 -+ Basic
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4.2 4.3
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Isomorphism between Tangle and Cobordism. Categories 3.1 Trading and Eliminating Handles Stratified Function Spaces and External Strands on W 3.2 3.3 From Tangle Classes to Cobordism Classes 3.4 Verification of Compositions
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categories and monoidal 2-categories
