Invariance Theory
The Heat Equation and the Atiyah-Singer Index Theorem| By: | Peter B. Gilkey |
| Publisher: | Taylor & Francis |
| Print ISBN: | 9780849378744 |
| eText ISBN: | 9781351436427 |
| Edition: | 1 |
| Copyright: | 1995 |
| Format: | Reflowable |
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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.