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Invariance Theory
The Heat Equation and the Atiyah-Singer Index Theorem
Overview
This book treats the Atiyah-Singer index theorem using the heat equation, which gives a local formula for the index of any elliptic complex.
Applications
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.
Methodology
The author uses invariance theory to identify the integrand of the index theorem for classical elliptic complexes with the invariants of the heat equation.
