Topological Quantum Field Theory and Four Manifolds
The present book is the first of its kind in dealing with topological quantum field theories and their applications to topological aspects of four manifolds. It is not only unique for this reason but also because it contains sufficient introductory materi
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Topological Quantum Field Theory and Four Manifolds
by
Jose Labastida Marcos Marino
TOPOLOGICAL QUANTUM FIELD THEORY AND FOUR MANIFOLDS
MATHEMATICAL PHYSICS STUDIES Editorial Board:
Maxim Kontsevich, IHES, Bures-sur-Yvette, France Massimo Porrati, New York University, New York, U.S.A. Vladimir Matveev, Université Bourgogne, Dijon, France Daniel Sternheimer, Université Bourgogne, Dijon, France
VOLUME 25
Topological Quantum Field Theory and Four Manifolds by
JOSE LABASTIDA and
MARCOS MARINO
A C.I.P. Catalogue record for this book is available from the Library of Congress.
ISBN 1-4020-3058-4 (HB) ISBN 1-4020-3177-7 (e-book)
Published by Springer, P.O. Box 17, 3300 AA Dordrecht, The Netherlands. Sold and distributed in North, Central and South America by Springer, 101 Philip Drive, Norwell, MA 02061, U.S.A. In all other countries, sold and distributed by Springer, P.O. Box 322, 3300 AH Dordrecht, The Netherlands.
Printed on acid-free paper
All Rights Reserved © 2005 Springer No part of this work may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, microfilming, recording or otherwise, without written permission from the Publisher, with the exception of any material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work. Printed in the Netherlands.
Table of Contents Preface
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1. Topological Aspects of Four-Manifolds . . . . . 1.1. Homology and cohomology . . . . . . . . 1.2. The intersection form . . . . . . . . . . 1.3. Self-dual and anti-self-dual forms . . . . . . 1.4. Characteristic classes . . . . . . . . . . . 1.5. Examples of four-manifolds. Complex surfaces 1.6. Spin and Spinc -structures on four-manifolds .
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2. The Theory of Donaldson Invariants . . 2.1. Yang–Mills theory on a four-manifold 2.2. SU (2) and SO(3) bundles . . . . . 2.3. ASD connections . . . . . . . . . 2.4. Reducible connections . . . . . . 2.5. A local model for the moduli space . 2.6. Donaldson invariants . . . . . . . 2.7. Metric dependence . . . . . . . .
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3. The Theory of Seiberg–Witten Invariants 3.1. The Seiberg–Witten equations . . . 3.2. The Seiberg–Witten invariants . . . 3.3. Metric dependence . . . . . . . .
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