Overview

This text examines the Atiyah-Singer theorem using the heat equation, which gives a local formula for the index of any elliptic complex. Heat equation methods are also used to discuss Lefschetz fixed point formulas, the Gauss-Bonnet theorem for a manifold with smooth boundary, and the geometrical theorem for a manifold with smooth boundary. The book presents a careful treatment of non-self-adjoint operators, asymptotics of the heat equation and variational formulas. It also introduces spectral geometry and provides a list of asymptotic formulas. The bibliography has been complied by Herbert Schroeder. The book is intended for applied mathematicians, mathematical physicists, engineering mechanics and materials scientists.

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9780849378744

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Gilkey, Peter B.

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