Invariance results for pairings with algebraic K-theory

2010/01/30 by Jens Kaad, Kaad, Jens
Mathematics · #19D55 #FOS: Mathematics #K-Theory and Homology (math.KT) #Operator Algebras (math.OA) #math.KT #math.OA #msc:19D55

paper · pdf · doi:10.48550/arxiv.1002.0053

arxiv created 2010/01/30 · arxiv updated 2010/02/26

Abstract

To each algebra over the complex numbers we associate a sequence of abelian groups in a contravariant functorial way. In degree (m-1) we have the m-summable Fredholm modules over the algebra modulo stable m-summable perturbations. These new finitely summable K-homology groups pair with cyclic homology and algebraic K-theory. In the case of cyclic homology the pairing is induced by the Chern-Connes character. The pairing between algebraic K-theory and finitely summable K-homology is induced by the Connes-Karoubi multiplicative character.

Related

• Cyclic Theory and the Bivariant Chern-Connes Character
• Characters of Fredholm modules and a problem of Connes
• A variant of algebraic K-theory
• Finitely Summable K-homology, the Index Pairing, and Cantor Minimal Systems
• Bass' NK groups and cdh-fibrant Hochschild homology