Mass endomorphism, surgery and perturbations

TL;DR

This paper demonstrates that the mass endomorphism linked to the Dirac operator is generally non-zero for most Riemannian metrics, using surgery, perturbation, and analysis near harmonic spinors.

Contribution

It establishes the generic non-vanishing of the mass endomorphism on Riemannian manifolds through new analytic and surgical techniques.

Findings

Mass endomorphism is non-zero for generic metrics.

Behavior of mass endomorphism under surgery analyzed.

Perturbation methods show stability near harmonic spinors.

Abstract

We prove that the mass endomorphism associated to the Dirac operator on a Riemannian manifold is non-zero for generic Riemannian metrics. The proof involves a study of the mass endomorphism under surgery, its behavior near metrics with harmonic spinors, and analytic perturbation arguments.