Atiyah-Singer index theorem
an introduction
Mukherjee, Amiya.
creator
text
xxu
New Delhi
Hindustan Book Agency
c2013
monographic
eng
xii, 267 p. ; 25 cm.
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.
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.
Amiya Mukherjee.
Includes bibliographical references and index.
Atiyah-Singer index theorem
Elliptic operators
Manifolds (Mathematics)
514.74 M953
Texts and readings in mathematics ; 69
9789380250540
ISI Library
160217
20160217104036.0
c26472
eng