Invariance Theory The Heat Equation and the Atiyah-Singer Index Theorem |
|
| Author:
| Gilkey, Peter B. |
| Series title: | Studies in Advanced Mathematics Ser. |
| ISBN: | 978-1-351-43641-0 |
| Publication Date: | May 2018 |
| Publisher: | Taylor & Francis Group
|
| Imprint: | CRC Press |
| Book Format: | Digital (delivered electronically) |
| List Price: | USD $250.00 |
Book Description:
|
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...
More DescriptionThis 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.