000			01944nam a22002777a 4500
999			_c58579 _d58579
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008			211112b ||||| |||| 00| 0 eng d
020			_a9789380250540
028			_a:9789380250540 _b:B-10 Street No 2 West Vinod Nagar Delhi 110092 _c:IM2892 _d:02/11/2021
082			_a514.74 MUK
100			_aMukherjee, Amiya
245			_aAtiyah-Singer index theorem _b : an introduction _c/ Amiya Mukherjee
260			_aNew Delhi _b: Hindustan Book Agency, _c©2013
300			_axii, 267 pages _c24cm.
365			_b600
490			_aTexts and readings in mathematics, 69.
505			_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.
520			_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,
650			_aMathematics
650			_a Topology
650			_aAtiyah-Singer index theorem.
650			_aElliptic operators.
650			_aFixed point theory.
700			_aMukherjee, Amiya
942			_cMDL