This collection of papers by leading researchers provides a broad picture of current research directions in index theory. Based on lectures presented at the NSF-CBMS Regional Conference on \(K\)-Homology and Index Theory, held in August 1991 at the University of Colorado at Boulder, the book provides both a careful exposition of new perspectives in classical index theory and an introduction to currently active areas of the field. Presented here are two new proofs of the classical Atiyah-Singer Index Theorem, as well as index theorems for manifolds with boundary and open manifolds. Index theory for semi-simple \(p\)-adic groups and the geometry of discrete groups are also discussed. Throughout the book, the application of operator algebras emerges as a central theme. Aimed at graduate students and researchers, this book is suitable as a text for an advanced graduate course on index theory.

Readership

Graduate students and researchers in index theory.

Table of Contents

• P. Baum, N. Higson, and R. Plymen -- Equivariant homology for \(SL(2)\) of a \(p\)-adic field
• E. Getzler -- Cyclic homology and the Atiyah-Patodi-Singer index theorem
• E. Guentner -- \(K\)-Homology and the index theorem
• N. Higson -- On the \(K\)-theory proof of the index theorem
• S. Hurder -- Topology of covers and the spectral theory of geometric operators
• R. Ji -- Some applications of cyclic cohomology to the study of group \(C^\ast\)-algebras
• P. Jorgensen -- Spectral theory for self-adjoint operator extensions associated with Clifford algebras
• D. Kucerovsky -- Averaging operators and open manifolds
• S. Zhang -- \(K\)-theory and a bivariable Fredholm index