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K-Theory for Operator Algebras
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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
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Journal ArticleDOI
The Rohlin Property for Shifts of Finite Type
TL;DR: In this article, it was shown that an automorphism of a unital AF C * -algebra with a certain approximate Rohlin property has the same property as the shift automorphisms associated with an irreducible shift of finite type.
Bivariant K- and Cyclic Theories
TL;DR: Bivariant K-theories generalize Ktheory and its dual, often called Khomology, at the same time as mentioned in this paper, and are a powerful tool for the computation of Ktheoretic invariants, for the formulation and proof of index theorems, for classification results and in many other instances.
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Differentiable absorption of Hilbert C*-modules, connections, and lifts of unbounded operators
TL;DR: In this article, a differentiable version of the Kasparov absorption theorem is proposed to construct densely defined connections (or correspondences) on Hilbert C*-modules, which can then be used to define selfadjoint and regular lifts of unbounded operators which act on an auxiliary Hilbert C *-module.
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Gauge theory on noncommutative Riemannian principal bundles
Branimir Ćaćić,Bram Mesland +1 more
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