Cyclic Cohomology of Etale Groupoids; The General Case

TL;DR

This paper develops a comprehensive method for calculating the cyclic cohomology of crossed product algebras associated with etale groupoids, broadening previous results by removing restrictions and including hyperbolic components, with applications to group actions and foliations.

Contribution

It extends the spectral sequence approach to compute cyclic cohomology for non-Hausdorff etale groupoids, including hyperbolic components and various examples.

Findings

Extended cyclic cohomology computations to non-Hausdorff groupoids.

Included hyperbolic components in the analysis.

Applied methods to group actions and foliations.

Abstract

We give a general method for computing the cyclic cohomology of crossed products by etale groupoids, extending the Feigin-Tsygan-Nistor spectral sequences. In particular we extend the computations performed by Brylinski, Burghelea,Connes and Nistor for the convolution algebra -of compactly supported smooth functions- of an etale groupoid, removing the Hausdorffness assumption and including the computation of the hyperbolic components. Examples like group actions on manifolds and foliations are considered.