Index theory of elliptic operators, foliations, and operator algebras : proceedings of the AMS special sessions held January 7, 1986 and April 11, 1986
著者
書誌事項
Index theory of elliptic operators, foliations, and operator algebras : proceedings of the AMS special sessions held January 7, 1986 and April 11, 1986
（Contemporary mathematics, v. 70）
American Mathematical Society, c1988
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注記
Includes bibliographies
"Special Session on Operator Algebras and Foliations was held at the 92nd Annual Meeting of the American Mathematical Society in New Orleans, Louisiana and the proceedings of the Special Session on Index Theory and its Applications was held at the 826th Meeting of the American Mathematical Society in Indianapolis, Indiana, April 11, 1986"--T.p. verso
内容説明・目次
内容説明
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.
目次
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.
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