Books by Peter B. (University of Oregon Gilkey

A great deal of progress has been made in the field of asymptotic formulas that arise in the theory of Dirac and Laplace type operators. This book collects these results and computations. It focuses on the functorial and special cases methods of computing asymptotic heat trace and heat content coefficients in the heat equation.

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.