James Humphreys (Chair)
2000 Mathematics Subject Classification. Primary 57R57, 57R19, 57R15, 58D27, 14J80,
53C55, 58J05, 58J52.
ABSTRACT. This text is intended to be an introduction to gauge theory and its applications in
geometry and topology. The goal is to present in great detail, and with many examples, a basic
collection of principles, techniques and applications needed to conduct independent research in
gauge theory. In particular, we present complete and self-contained computations of the Seiberg-
Witten invariants of most simply connected algebraic surfaces and we discuss at great length a new
approach to cutting and pasting of Seiberg-Witten invariants. Familiarity with basic algebraic
topology and differential geometry is assumed.
Librar y of Congress Cataloging-in-Publication D a t a
Nicolaescu, Liviu I.
Notes on Seiberg-Witten theory / Liviu I. Nicolaescu.
p. cm. — (Graduate studies in mathematics ; v. 28)
Includes bibliographical references and index.
1. Seiberg-Witten invariants. 2. Global analysis. 3. Four-manifolds (Topology) 4. Mathe-
matical physics. I. Title. II. Series.
Copying an d reprinting. Individual readers of this publication, and nonprofit libraries
acting for them, are permitted to make fair use of the material, such as to copy a chapter for use
in teaching or research. Permission is granted to quote brief passages from this publication in
reviews, provided the customary acknowledgment of the source is given.
Republication, systematic copying, or multiple reproduction of any material in this publication
is permitted only under license from the American Mathematical Society. Requests for such
permission should be addressed to the Assistant to the Publisher, American Mathematical Society,
P. O. Box 6248, Providence, Rhode Island 02940-6248. Requests can also be made by e-mail to
© 2000 by the American Mathematical Society. All rights reserved.
The American Mathematical Society retains all rights
except those granted to the United States Government.
Printed in the United States of America.
@ The paper used in this book is acid-free and falls within the guidelines
established to ensure permanence and durability.
Visit the AMS home page at URL: http://www.ams.org/
10 9 8 7 6 5 4 3 2 1 05 04 03 02 01 00