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Atiyah-Singer index theorem : an introduction / Amiya Mukherjee.

By: Mukherjee, Amiya.
Material type: TextTextSeries: Texts and readings in mathematics ; 69.Publisher: New Delhi : Hindustan Book Agency, c2013Description: xii, 267 p. ; 25 cm.ISBN: 9789380250540.Subject(s): Atiyah-Singer index theorem | Elliptic operators | Manifolds (Mathematics)DDC classification: 514.74
Contents:
1. K-theory -- 2. Fredholm operators and Atiyah-Jänich theorem -- 3. Bott periodicity and Thom isomorphism -- 4. Pseudo-differential operators -- 5. Characteristic classes and Chern-Weil construction -- 6. Spin structure and Dirac operator -- 7. Equivariant k-theory -- 8. The index theorem -- 9. Cohomological formulation of the index theorem -- Bibliography -- Index.
Summary: 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.
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Includes bibliographical references and index.

1. K-theory --
2. Fredholm operators and Atiyah-Jänich theorem --
3. Bott periodicity and Thom isomorphism --
4. Pseudo-differential operators --
5. Characteristic classes and Chern-Weil construction --
6. Spin structure and Dirac operator --
7. Equivariant k-theory --
8. The index theorem --
9. Cohomological formulation of the index theorem --
Bibliography --
Index.

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.

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