The index of a transverse Dirac-type operator: the case of abelian Molino sheaf

TL;DR

This paper derives a local formula for the index of a transverse Dirac-type operator on a compact Riemannian foliated manifold, assuming the Molino sheaf is abelian, advancing understanding in geometric analysis.

Contribution

It provides a new local index formula specifically for cases where the Molino sheaf is abelian, which was not previously established.

Findings

Derived a local index formula for abelian Molino sheaf cases

Extended index theory to Riemannian foliations with abelian Molino sheaves

Clarified the structure of transverse Dirac operators in this setting

Abstract

We give a local formula for the index of a transverse Dirac-type operator on a compact manifold with a Riemannian foliation, under the assumption that the Molino sheaf is a sheaf of abelian Lie algebras.