Index theorems on manifolds with straight ends
Werner Ballmann (UNIVERSITAT BONN, M.P.I.M.), Jochen Br\"uning, (HUMBOLDT UNIVERSITAT), Gilles Carron (LMJL)

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.
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