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.
Equivariant homology for $SL(2)$ of a $p$-adic field by P. Baum, N. Higson, and R. Plymen Cyclic homology and the Atiyah-Patodi-Singer index theorem by E. Getzler $K$-Homology and the index theorem by E. Guentner On the $K$-theory proof of the index theorem by N. Higson Topology of covers and the spectral theory of geometric operators by S. Hurder Some applications of cyclic cohomology to the study of group $C^\ast$-algebras by R. Ji Spectral theory for self-adjoint operator extensions associated with Clifford algebras by P. Jorgensen Averaging operators and open manifolds by D. Kucerovsky $K$-theory and a bivariable Fredholm index by S. Zhang.
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- ID: 9780821851524
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