Excision in bivariant periodic cyclic cohomology
type: Item
instance of: scholarly article
title: Excision in bivariant periodic cyclic cohomology
zbMATH Open document ID: 0889.46054
author: Joachim Cuntz
author: Daniel Gray Quillen
published in: Inventiones Mathematicae
publication date: 1998-06-01T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 46L80
Mathematics Subject Classification ID: 46M20
Mathematics Subject Classification ID: 55N40
Mathematics Subject Classification ID: 55S25
zbMATH DE Number: 1026496
zbMATH Keywords: excision property
zbMATH Keywords: bivariant, periodic, cyclic homology/cohomology
zbMATH Keywords: six term exact sequence
zbMATH Keywords: filtered supercomplexes
zbMATH Keywords: quasi-free extensions
zbMATH Keywords: \(K\)-theory
zbMATH Keywords: pro-algebras
zbMATH Keywords: supercomplexes
zbMATH Keywords: bivariant periodic cyclic theory
zbMATH Keywords: Chern character map
zbMATH Keywords: periodic cyclic cohomology
reviewed by: Vasile Oproiu
MaRDI profile type: Publication
full work available at URL: s002220050115
OpenAlex ID: W2073123306
Wikidata QID: Q101086132
DOI: 10.1007/S002220050115
description: scientific article; zbMATH DE number 1026496