eBook ISBN:  9780821876596 
Product Code:  CONM/70.E 
List Price:  $125.00 
MAA Member Price:  $112.50 
AMS Member Price:  $100.00 
eBook ISBN:  9780821876596 
Product Code:  CONM/70.E 
List Price:  $125.00 
MAA Member Price:  $112.50 
AMS Member Price:  $100.00 

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 nonpositive 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.

Table of Contents

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 finitedimensional 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 “CWcomplexes” [ 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 nonpositive 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 finitedimensional 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 “CWcomplexes” [ MR 948697 ]