Invariance Theory

The Heat Equation and the Atiyah-Singer Index Theorem

af Peter B. (University of Oregon Gilkey

Treats the Atiyah-Singer index theorem using the heat equation, which gives a local formula for the index of any elliptic complex. This work also uses heat equation methods 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.