| eBook ISBN: | 978-0-8218-7659-6 |
| Product Code: | CONM/70.E |
| List Price: | $125.00 |
| MAA Member Price: | $112.50 |
| AMS Member Price: | $100.00 |
| eBook ISBN: | 978-0-8218-7659-6 |
| Product Code: | CONM/70.E |
| List Price: | $125.00 |
| MAA Member Price: | $112.50 |
| AMS Member Price: | $100.00 |
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Book DetailsContemporary MathematicsVolume: 70; 1988; 336 ppMSC: Primary 46; Secondary 00; 57; 58
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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Table of Contents
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Articles
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John Cantwell and Lawrence Conlon — The theory of levels [ MR 948686 ]
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Ronald G. Douglas, Steven Hurder and Jerome Kaminker — Toeplitz operators and the eta invariant: the case of $S^1$ [ MR 948687 ]
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Thierry Fack — Sur la conjecture de Novikov [ MR 948688 ]
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Jeff Fox and Peter Haskell — A new proof of the $K$-amenability of ${\rm SU}(1,1)$ [ MR 948689 ]
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James L. Heitsch — Some interesting group actions [ MR 948690 ]
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Connor Lazarov — A relation between index and exotic classes [ MR 948691 ]
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Ib Madsen and Jonathan Rosenberg — The universal coefficient theorem for equivariant $K$-theory of real and complex $C^*$-algebras [ MR 948692 ]
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N. Christopher Phillips — Equivariant $K$-theory for proper actions and $C^*$-algebras [ MR 948693 ]
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N. Christopher Phillips — Equivariant $K$-theory for proper actions. II. Some cases in which finite-dimensional bundles suffice [ MR 948694 ]
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John Roe — Operator algebras and index theory on noncompact manifolds [ MR 948695 ]
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Jonathan Rosenberg — $K$-theory of group $C^*$-algebras, foliation $C^*$-algebras, and crossed products [ MR 948696 ]
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Xiaolu Wang — Noncommutative “CW-complexes” [ MR 948697 ]
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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.
-
Articles
-
John Cantwell and Lawrence Conlon — The theory of levels [ MR 948686 ]
-
Ronald G. Douglas, Steven Hurder and Jerome Kaminker — Toeplitz operators and the eta invariant: the case of $S^1$ [ MR 948687 ]
-
Thierry Fack — Sur la conjecture de Novikov [ MR 948688 ]
-
Jeff Fox and Peter Haskell — A new proof of the $K$-amenability of ${\rm SU}(1,1)$ [ MR 948689 ]
-
James L. Heitsch — Some interesting group actions [ MR 948690 ]
-
Connor Lazarov — A relation between index and exotic classes [ MR 948691 ]
-
Ib Madsen and Jonathan Rosenberg — The universal coefficient theorem for equivariant $K$-theory of real and complex $C^*$-algebras [ MR 948692 ]
-
N. Christopher Phillips — Equivariant $K$-theory for proper actions and $C^*$-algebras [ MR 948693 ]
-
N. Christopher Phillips — Equivariant $K$-theory for proper actions. II. Some cases in which finite-dimensional bundles suffice [ MR 948694 ]
-
John Roe — Operator algebras and index theory on noncompact manifolds [ MR 948695 ]
-
Jonathan Rosenberg — $K$-theory of group $C^*$-algebras, foliation $C^*$-algebras, and crossed products [ MR 948696 ]
-
Xiaolu Wang — Noncommutative “CW-complexes” [ MR 948697 ]
