Equivariant KK -theory and the Novikov conjecture

Operators on Hilbert Space.- C*-Algebras.- Von Neumann Algebras.- Further Structure.- K-Theory and Finiteness.

Operator Algebras: Theory of C*-Algebras and von Neumann Algebras

An overview of the integer quantum Hall effect is given. A mathematical framework using nonommutative geometry as defined by Connes is prepared. Within this framework, it is proved that the Hall conductivity is quantized and that plateaux occur when the Fermi energy varies in a region of localized states.

The noncommutative geometry of the quantum Hall effect

C∗-algebras of real rank zero

Locally compact groups Dynamical systems and crossed products Special cases and basic constructions Imprimitivity theorems Induced representations and induced ideals Orbits and quasi-orbits Properties of crossed products Ideal structure The proof of the Gootman-Rosenberg-Sauvageot theorem Amenable groups The Banach *-algebra $L^1(G,A)$ Bundles of $C*$-algebras Groups Representations of $C*$-algebras Direct integrals Effros's ideal center decomposition The Fell topology Miscellany Notation and Symbol Index Index Bibliography.

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Crossed products of C*-algebras

I. Introduction To K-Theory.- 1. Survey of topological K-theory.- 2. Overview of operator K-theory.- II. Preliminaries.- 3. Local Banach algebras and inductive limits.- 4. Idempotents and equivalence.- III. K0-Theory and Order.- 5. Basi K0-theory.- 6. Order structure on K0.- 7. Theory of AF algebras.- IV. K1-Theory and Bott Periodicity.- 8. Higher K-groups.- 9. Bott Periodicity.- V. K-Theory of Crossed Products.- 10. The Pimsner-Voiculescu exact sequence and Connes' Thorn isomorphism.- 11. Equivariant K-theory.- VI. More Preliminaries.- 12. Multiplier algebras.- 13. Hilbert modules.- 14. Graded C*-algebras.- VII. Theory of Extensions.- 15. Basic theory of extensions.- 16. Brown-Douglas-Fillmore theory and other applications.- VIII. Kasparov's KK-Theory.- 17. Basic theory.- 18. Intersection product.- 19. Further structure in KK-theory.- 20. Equivariant KK-theory.- IX. Further Topics.- 21. Homology and cohomology theories on C*-algebras.- 22. Axiomatic K-theory.- 23. Universal coefficient theorems and Kunneth theorems.- 24. Survey of applications to geometry and topology.

K-Theory for Operator Algebras

Dimension functions and traces on C∗-algebras

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Bruce Blackadar

Papers

K-Theory for Operator Algebras

Operator Algebras: Theory of C*-Algebras and von Neumann Algebras

Dimension functions and traces on C∗-algebras

Shape theory for $C^*$-algebras.

Generalized inductive limits of finite-dimensional C*-algebras