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Bivariant Chern character and the longitudinal index theory

Alexander Gorokhovsky
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Abstract

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 $Φ$ 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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Alexander Gorokhovsky. 2005-04-06. Bivariant Chern character and the longitudinal index theory. https://arxiv.org/abs/math/0504092

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