Open AccessBook
K-Theory for Operator Algebras
Reads0
Chats0
TLDR
A survey of topological K-theory can be found in this paper, where the authors present a survey of applications to geometry and topology, including the Pimsner-Voiculescu exact sequence and Connes' Thorn isomorphism.Abstract:
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.read more
Citations
More filters
Posted Content
What is geometry in quantum theory
TL;DR: In this paper, the authors briefly survey some peculiarities of geometric techniques in quantum models, and present a survey of geometric methods in modern physics for quantum models with respect to the first issue of International Journal of Geometric Methods in Modern Physics.
Journal ArticleDOI
The K-theory and the invertibility of almost periodic Toeplitz operators
TL;DR: In this paper, the authors use K-theory to study the invertibility of systems of almost periodic Toeplitz operators and show that they are invertible.
Journal ArticleDOI
The signature operator at 2
TL;DR: In this article, the signature operator on a manifold defines a K-homology class which is an orientation after inverting 2, and what special properties does this class have, and it is well known that it is bordism invariant.
Posted Content
Some classifiable groupoid C*-algebras with prescribed K-theory
TL;DR: In this article, a minimal, amenable, etale equivalence relation on a Cantor set whose associated groupoid is tracially AF, and hence classifiable in the Elliott classification scheme, was constructed.