A bivariant Chern character for families of spectral triples

Abstract

In this paper we construct a bivariant Chern character defined on ``families of spectral triples''. Such families should be viewed as a version of unbounded Kasparov bimodules adapted to the category of bornological algebras. The Chern character then takes its values in the bivariant entire cyclic cohomology of Meyer. The basic idea is to work within Quillen's algebra cochains formalism, and construct the Chern character from the exponential of the curvature of a superconnection, leading to a heat kernel regularization of traces. The obtained formula is a bivariant generalization of the JLO cocycle.

54 pages, LaTex

References in corpus (8)

• D-Branes And K-Theory
• Hopf algebras, cyclic cohomology and the transverse index theory
• Analytic cyclic cohomology
• Characters of Cycles, Equivariant Characteristic Classes and Fredholm Modules
• Twisted K-homology theory, twisted Ext-theory
• Cyclic cohomology and Hopf algebras
• BRS Cohomology And The Chern Character In Non-Commutative Geometry
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Cited by in corpus (4)

• Entire cyclic homology of continuous trace algebras
• Chern character, Hopf algebras, and BRS cohomology
• Sur les formules locales de l'indice
• Secondary invariants for Frechet algebras, quasihomomorphisms, and the residue Chern character