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  3. Invariance Theory: The Heat Equation and the Atiyah-Singer Index Theorem

Invariance Theory: The Heat Equation and the Atiyah-Singer Index Theorem

Posted By: arundhati
Date: 29 Aug 2018 15:59:35
Invariance Theory: The Heat Equation and the Atiyah-Singer Index Theorem

Peter B. Gilkey, "Invariance Theory: The Heat Equation and the Atiyah-Singer Index Theorem"
1995 | ISBN-10: 0849378745 | 536 pages | PDF | 21 MB

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.
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