Bivariant Chern character and the longitudinal index theory

Details Bivariant Chern character and the longitudinal index theory Bivariant Chern character and the longitudinal index theory

2005-04-06

arxiv.org/abs/math/0504092v1

Mathematics

Differential Geometry

Scientific paper

In this paper we consider a family of Dirac-type operators on fibration $P \to B$ equivariant with respect to an action of an etale groupoid. Such a family defines an element in the bivariant $K$ theory. We compute the action of the bivariant Chern character of this element on the image of Connes' map $\Phi$ in the cyclic cohomology. A particular case of this result is Connes' index theorem for etale groupoids in the case of fibrations.

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