On the algebraic index for riemannian étale groupoids

Abstract

In this paper we construct an explicit quasi-isomorphism to study the cyclic cohomology of a deformation quantization over a riemannian étale groupoid. Such a quasi-isomorphism allows us to propose a general algebraic index problem for riemannian étale groupoids. We discuss solutions to that index problem when the groupoid is proper or defined by a constant Dirac structure on a 3-dim torus.

19 pages