Combining analysis, geometry, and topology, this volume provides an introduction to current ideas involving the application of $K$-theory of operator algebras to index theory and geometry. In particular, the articles follow two main themes: the use of operator algebras to reflect properties of geometric objects and the application of index theory in settings where the relevant elliptic operators are invertible modulo a $C^*$-algebra other than that of the compact operators. The papers in this collection are the proceedings of the special sessions held at two AMS meetings: the Annual meeting in New Orleans in January 1986, and the Central Section meeting in April 1986. Jonathan Rosenberg's exposition supplies the best available introduction to Kasparov's $KK$-theory and its applications to representation theory and geometry.A striking application of these ideas is found in Thierry Fack's paper, which provides a complete and detailed proof of the Novikov Conjecture for fundamental groups of manifolds of non-positive curvature. Some of the papers involve Connes' foliation algebra and its $K$-theory, while others examine $C^*$-algebras associated to groups and group actions on spaces.
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Zielgruppe
Für höhere Schule und Studium
Für Beruf und Forschung
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Höhe: 254 mm
Breite: 171 mm
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ISBN-13
978-0-8218-5077-0 (9780821850770)
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Schweitzer Klassifikation
The theory of levels by J. Cantwell and L. Conlon Toeplitz operators and the eta invariant: the case of $S^1$ by R. G. Douglas, S. Hurder, and J. Kaminker Sur la Conjecture de Novikov by T. Fack A new proof of the $K$-amenability of $SU(1,1)$ by J. Fox and P. Haskell Some interesting group actions by J. L. Heitsch A relation between index and exotic classes by C. Lazarov The Universal Coefficient Theorem for equivariant $K$-theory of real and complex $C^*$-algebras by I. Madsen and J. Rosenberg Equivariant $K$-theory for proper actions and $C^*$-algebras by N. C. Phillips Equivariant $K$-theory for proper actions II: some cases in which finite dimensional bundles suffice by N. C. Phillips Operator algebras and index theory on non-compact manifolds by J. Roe $K$-theory of group $C^*$-algebras, foliation algebras and crossed products by J. Rosenberg Non-commutative $CW$-complexes by X. Wang.
