http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
the heat equation and the atiyah-singer index theorem
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.
chapter 1 Pseudo-differential operators -- chapter 2 Characteristic classes -- chapter 3 The index theorem -- chapter 4 Spectral geom etry -- chapter 5 Bibliographic information.