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Atiyah-Singer Index Theorem: An Introduction
Amiya Mukherjee, Indian Statistical Institute, Calcutta, India
A publication of Hindustan Book Agency.
cover
Hindustan Book Agency
2013; 276 pp; hardcover
ISBN-13: 978-93-80250-54-0
List Price: US$60
Member Price: US$48
Order Code: HIN/64
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This monograph is a thorough introduction to the Atiyah-Singer index theorem for elliptic operators on compact manifolds without boundary. The main theme is only the classical index theorem and some of its applications, but not the subsequent developments and simplifications of the theory.

The book is designed for a complete proof of the \(K\)-theoretic index theorem and its representation in terms of cohomological characteristic classes. In an effort to make the demands on the reader's knowledge of background materials as modest as possible, the author supplies the proofs of almost every result. The applications include Hirzebruch signature theorem, Riemann-Roch-Hirzebruch theorem, and the Atiyah-Segal-Singer fixed point theorem, etc.

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 \(K\)-theoretic index theorem.

Table of Contents

  • \(K\)-theory
  • Fredholm operators and Atiyah-Jädnich theorem
  • Bott periodicity and Thom isomorphism
  • Pseudo-differential operators
  • Characteristic classes and Chern-Weil construction
  • Spin structure and Dirac operator
  • Equivariant \(K\)-theory
  • The index theorem
  • Cohomological formulation of the index theorem
  • Bibliography
  • Index
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