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Chapman and Hall/CRC Elliptic Operators and Topology Book

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Description

This research note from the Pitman Research Notes in Mathematics series provides an introduction to the concepts surrounding the heat equation proof of the Atiyah-Singer index theorem. It explores how asymptotic expansions for solutions of partial differential equations on compact manifolds are used to obtain topological information through a supersymmetric cancellation of eigenspaces. The analysis focuses on Dirac operators on Clifford bundles. This mathematical text includes detailed proofs for the Hodge theorem, eigenvalue estimates, the Lefschetz theorem, the index theorem, and the Morse inequalities. Practical examples are included to illustrate the general theory, making it a valuable resource for studying the connection between analysis and topology.

Key Features

This Chapman and Hall/CRC publication covers the heat equation proof of the Atiyah-Singer index theorem.

The text uses asymptotic expansions for partial differential equation solutions on compact manifolds to derive topological information.

Mathematical analysis is presented within the specific context of Dirac operators on Clifford bundles.

Included proofs cover the Hodge theorem, eigenvalue estimates, the Lefschetz theorem, and the index theorem.

The book provides the Morse inequalities and uses examples to illustrate the general theory of the subject.

Product Specifications

Format
paperback
Domain
Amazon UK
Release Date
06 January 1999
Listed Since
05 February 2007

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