01866nam a22002417a 4500001000700000003002100007005001700028008004100045020001800086040002100104082002100125100002200146245007200168260004800240300002700288490004600315504005100361505037600412520074800788650003401536650002601570650002801596c26472ISI Library, Kolkata20160217104036.0160217b xxu||||| |||| 00| 0 eng d a9789380250540 aISI Librarybeng04a514.74223bM9531 aMukherjee, Amiya.10aAtiyah-Singer index theorem : ban introduction /cAmiya Mukherjee. aNew Delhi :bHindustan Book Agency,cc2013. axii, 267 p. ;c25 cm. 0 a Texts and readings in mathematics ;v69. aIncludes bibliographical references and index.0 a1. 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. aThis 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. 0aAtiyah-Singer index theorem. 0aElliptic operators. 0aManifolds (Mathematics)