A bivariant Chern character for families of spectral triples

Details A bivariant Chern character for families of spectral triples A bivariant Chern character for families of spectral triples

2001-03-12

arxiv.org/abs/math-ph/0103016v3

Commun.Math.Phys. 231 (2002) 45-95

Physics

Mathematical Physics

54 pages, LaTex

Scientific paper

10.1007/s00220-002-0672-9

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.

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