AtiyahSinger index theorem : an introduction / Amiya Mukherjee.
By: Mukherjee, Amiya.
Material type: TextSeries: Texts and readings in mathematics ; 69.Publisher: New Delhi : Hindustan Book Agency, c2013Description: xii, 267 p. ; 25 cm.ISBN: 9789380250540.Subject(s): AtiyahSinger index theorem  Elliptic operators  Manifolds (Mathematics)DDC classification: 514.74Item type  Current location  Call number  Status  Date due  Barcode  Item holds  

Books 
ISI Library, Kolkata

514.74 M953 (Browse shelf)  Available  C26472 
Includes bibliographical references and index.
1. Ktheory 
2. Fredholm operators and AtiyahJänich theorem 
3. Bott periodicity and Thom isomorphism 
4. Pseudodifferential operators 
5. Characteristic classes and ChernWeil construction 
6. Spin structure and Dirac operator 
7. Equivariant ktheory 
8. The index theorem 
9. Cohomological formulation of the index theorem 
Bibliography 
Index.
This monograph is a thorough introduction to the AtiyahSinger 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, RiemannRochHirzebruch theorem, and the AtiyahSegalSinger fixed point theorem, etc.
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