Excision in bivariant periodic cyclic cohomology
The authors present a general framework for an excision property for bivariant, periodic, cyclic homology/cohomology (i.e. the existence of a six term exact sequence). First, they present a theory of cyclic homology, based on filtered supercomplexes and quasi-free extensions. Then it is obtained an extension of cyclic homology to the category of pro-algebras and the use of pro-complexes. Finally, it is obtained the excision in both variables in the case of the bivariant periodic cyclic theory \(HP^*(A,B)\) (where \(A,B\) are pro-algebras). The connecting maps in the long exact sequences are given as composition products with the fundamental class in \(HP^1\), of extension. Then it is obtained a completely general bivariant Chern character. This Chern character map is an isomorphism in the case of a large class of topological algebras. Some interesting applications are presented, in the case of periodic cyclic cohomology.
bivariant, periodic, cyclic homology/cohomology
scientific article; zbMATH DE number 1026496