Local index theory over foliation groupoids

TL;DR

This paper presents a superconnection proof of an index theorem for Dirac-type operators invariant under foliation groupoid actions, advancing the mathematical understanding of index theory in the context of foliation groupoids.

Contribution

It introduces a novel superconnection proof of the index theorem specifically for Dirac-type operators invariant under foliation groupoids.

Findings

Established a superconnection-based proof of the index theorem.

Extended index theory to operators invariant under foliation groupoid actions.

Provided mathematical tools for analyzing Dirac operators in foliation contexts.

Abstract

We give a superconnection proof of an index theorem for a Dirac-type operator that is invariant with respect to the action of a foliation groupoid.