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# Invariance Theory, the Heat Equation, and the Atiyah-Singer Index Theorem

DOI link for Invariance Theory, the Heat Equation, and the Atiyah-Singer Index Theorem

Invariance Theory, the Heat Equation, and the Atiyah-Singer Index Theorem book

# Invariance Theory, the Heat Equation, and the Atiyah-Singer Index Theorem

DOI link for Invariance Theory, the Heat Equation, and the Atiyah-Singer Index Theorem

Invariance Theory, the Heat Equation, and the Atiyah-Singer Index Theorem book

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## ABSTRACT

This book treats the Atiyah-Singer index 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 author uses invariance theory to identify the integrand of the index theorem for classical elliptic complexes with the invariants of the heat equation.