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
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.