Elliptic Operators, Topology, and Asymptotic Methods

The index theorem continues to stand as a central result of modern mathematics. In a concise presentation that offers streamlined analyses and coverage of important examples and applications, this book introduces the ideas surrounding the heat equation proof of the Atiyah-Singer index theorem. It assumes some background in differential geometry and functional analysis. With the partial differential equation theory developed within the text and the exercises in each chapter, this becomes the ideal vehicle for self-study or coursework. Anyone working with index theory or supersymmetry will find it a succinct but wide-ranging introduction to this important and intriguing field.