An index formula in a class of groupoid C∗-algebras

Abstract

We consider the groupoid $C^{\ast }$-algebra $\mathcal{T}=C^{\ast }(\mathcal{G})$, where the groupoid $\mathcal{G}$ is a reduction of a transformation group $\mathcal{G}=(Y\times G)|X$, and $Y$

and $X$ are suitable topological spaces. We impose additional constraints on a cross-section $\psi$, which gives opportunity to define cyclic 1-cocycle and to obtain a formula that calculates the index of the Fredholm operators.