Contemporary Mathematics 1993; 190 pp; softcover Volume: 148 ISBN10: 0821851527 ISBN13: 9780821851524 List Price: US$49 Member Price: US$39.20 Order Code: CONM/148
 This collection of papers by leading researchers provides a broad picture of current research directions in index theory. Based on lectures presented at the NSFCBMS 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 AtiyahSinger Index Theorem, as well as index theorems for manifolds with boundary and open manifolds. Index theory for semisimple \(p\)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 AtiyahPatodiSinger 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 selfadjoint operator extensions associated with Clifford algebras
 D. Kucerovsky  Averaging operators and open manifolds
 S. Zhang  \(K\)theory and a bivariable Fredholm index
