Kasparov's bivariant Ktheory

General Introduction
<]]> 
Search results
<]]> 
Online References
<]]> 
Paper References
<]]> 
Definition
<]]> 
Properties
<]]> 
Standard theorems
<]]> 
Open Problems
<]]> 
Connections to Number Theory
<]]> 
Computations and Examples
<]]> 
History and Applications
<]]> 
Some Research Articles
arXiv:1206.0178 Algebraic Kasparov Ktheory. II from arXiv Front: math.AT by Grigory Garkusha A kind of motivic stable homotopy theory of algebras is developed. Explicit fibrant replacements for the S^1spectrum and (S^1,\G)bispectrum of an algebra are constructed. As an application, unstable, Morita stable and stable universal bivariant theories are recovered. These are shown to be embedded by means of contravariant equivalences as full triangulated subcategories of compact generators of some compactly generated triangulated categories. Another application is to introduce and study the symmetric monoidal compactly generated triangulated category of Kmotives. It is established that the triangulated category kk of CortinasThom can be identified with Kmotives of algebras. It is proved that the triangulated category of Kmotives is a localization of the triangulated category of (S^1,\G)bispectra. Also, explicit fibrant (S^1,\G)bispectra representing stable algebraic Kasparov Ktheory and algebraic homotopy Ktheory are constructed.
<]]> 
Other Information
<]]> 
Comments Posted
<]]> 
Comments
There are no comments.