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

✍ Scribed by Gilkey P.B.

• Book ID: 127398793
• Year: 1996
• Tongue: English
• Weight: 819 KB
• Category: Library

✦ Synopsis

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.