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Seiberg-Witten Gauge Theory
Matilde Marcolli, Massachusetts Institute of Technology, Cambridge, MA
A publication of Hindustan Book Agency.
Hindustan Book Agency
1999; 228 pp; hardcover
ISBN-10: 81-85931-22-4
ISBN-13: 978-81-85931-22-7
List Price: US$52
Member Price: US$41.60
Order Code: HIN/6
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The newly developed field of Seiberg-Witten gauge theory has become a well-established part of the differential topology of four-manifolds and three-manifolds. This book offers an introduction and an up-to-date review of the state of current research.

The first part of the book collects some preliminary notions and then gives an introduction of Seiberg-Witten theory of four-dimensional manifolds. In the second part, the author introduces the dimensional reduction and uses it to describe Seiberg-Witten in three-dimensional manifolds. In both parts, the Seiberg-Witten equations are derived, the moduli spaces of solutions are constructed, and the corresponding invariants of manifolds are introduced.

In the third part, the author gives an overview of geometric and topological results obtained via Seiberg-Witten theory. Through all these parts of the book, Seiberg-Witten gauge theory is considered as a completely self-contained subject and no a priori knowledge of Donaldson theory is assumed. In fact, all the sections that refer to Donaldson theory can be skipped, and this will not affect the comprehension of the remaining sections.

In the final part of the book, the author describes physical theories that are responsible for the emergence of this new piece of mathematics, the Seiberg-Witten theory.

A publication of Hindustan Book Agency; distributed within the Americas by the American Mathematical Society. Maximum discount of 20% for all commercial channels.

Readership

Graduate students and research mathematicians interested in geometry of manifolds and gauge theory.

Table of Contents

  • Introduction
  • Seiberg-Witten on four-manifolds
  • Seiberg-Witten on three-manifolds
  • Topology and geometry
  • Seiberg-Witten and physics
  • Appendix: a bibliographical guide
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