A note on invertibility of the Dirac operator twisted with Hilbert-A-module coefficients

TL;DR

This paper proves that on a closed spin manifold with non-negative scalar curvature, the Dirac operator twisted with any flat Hilbert module bundle is always invertible, highlighting a key geometric-analytic property.

Contribution

It establishes the invertibility of the twisted Dirac operator under specific curvature conditions, extending previous results to flat Hilbert module bundles.

Findings

Twisted Dirac operator is invertible on manifolds with positive scalar curvature.

Invertibility holds for any flat Hilbert module bundle.

Results connect geometric curvature conditions with operator invertibility.

Abstract

Given a closed connected spin manifold M with non-negative and somewhere positive scalar curvature, we show that the Dirac operator twisted with any flat Hilbert module bundle is invertible.