Index theorems on manifolds with straight ends

TL;DR

This paper investigates the Fredholm properties and index formulas of Dirac operators on complete Riemannian manifolds with straight ends, including those with pinched negative curvature and finite volume, expanding understanding of geometric analysis on such spaces.

Contribution

It provides new index formulas and Fredholm criteria for Dirac operators on manifolds with straight ends, a class not extensively studied before.

Findings

Established Fredholm criteria for Dirac operators on manifolds with straight ends.

Derived explicit index formulas for these operators.

Applied results to manifolds with pinched negative curvature and finite volume.

Abstract

We study Fredholm properties and index formulas for Dirac operators over complete Riemannian manifolds with straight ends. An important class of examples of such manifolds are complete Riemannian manifolds with pinched negative sectional curvature and finite volume.