Atiyah-Singer index theorem
Mukherjee, Amiya
Atiyah-Singer index theorem : an introduction / Amiya Mukherjee - New Delhi : Hindustan Book Agency, ©2013 - xii, 267 pages 24cm. - Texts and readings in mathematics, 69. .
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.
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,
9789380250540
9789380250540 :B-10 Street No 2 West Vinod Nagar Delhi 110092
Mathematics
Topology
Atiyah-Singer index theorem.
Elliptic operators.
Fixed point theory.
514.74 MUK
Atiyah-Singer index theorem : an introduction / Amiya Mukherjee - New Delhi : Hindustan Book Agency, ©2013 - xii, 267 pages 24cm. - Texts and readings in mathematics, 69. .
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.
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,
9789380250540
9789380250540 :B-10 Street No 2 West Vinod Nagar Delhi 110092
Mathematics
Topology
Atiyah-Singer index theorem.
Elliptic operators.
Fixed point theory.
514.74 MUK
