Atiyah-Singer Index Theorem

Atiyah-Singer Index Theorem Synopsis

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, with an effort to make the demands on the knowledge of background materials as modest as possible by supplying the proofs of all most every result.

The applications include Hirzebruch signature theorem, Riemann-Roch-Hirzebruch theorem, Atiyah-Segal-Singer fixed point theorem, etc.