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Notes on Seiberg-Witten Theory
Liviu I. Nicolaescu, University of Notre Dame, IN
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Graduate Studies in Mathematics
2000; 484 pp; hardcover
Volume: 28
ISBN-10: 0-8218-2145-8
ISBN-13: 978-0-8218-2145-9
List Price: US$68
Member Price: US$54.40
Order Code: GSM/28
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In this volume the author presents, in great detail and with many examples, a basic collection of principles, techniques, and applications needed to conduct independent research in gauge theory and its use in geometry and topology. Complete and self-contained computations of the Seiberg-Witten invariants of most simply connected algebraic surfaces using only Witten's factorization method are included. Also given is a new approach to cutting and pasting Seiberg-Witten invariants, which is illustrated by examples such as the connected sum theorem, the blow-up formula, and a proof of a vanishing result of Fintushel and Stern. The book is a suitable textbook for advanced graduate courses in differential geometry, algebraic topology, basic PDEs and functional analysis.

Readership

Graduate students and research mathematicians interested in geometry and topology.

Table of Contents

  • Preliminaries
  • The Seiberg-Witten invariants
  • Seiberg-Witten equations on complex surfaces
  • Gluing techniques
  • Epilogue
  • Bibliography
  • Index
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