Perturbations of basic Dirac operators on Riemannian foliations

TL;DR

This paper employs Witten deformation to relate the basic index of a transversal Dirac operator on Riemannian foliations to integers linked to critical leaf closures, providing a new computational approach.

Contribution

It introduces a novel method to compute the basic index of Dirac operators on Riemannian foliations using Witten deformation and critical leaf closures.

Findings

Expresses the basic index as a sum over critical leaf closures.

Connects the index to integers associated with leaf closures.

Provides a new technique for analyzing Dirac operators on foliations.

Abstract

Using the method of Witten deformation, we express the basic index of a transversal Dirac operator over a Riemannian foliation as the sum of integers associated to the critical leaf closures of a given foliated bundle map.