Abstract cone operators and Lipschitz rigidity for scalar curvature on singular manifolds

07.08.2025, 16:15  –  Haus 9, Raum 1.22
Forschungsseminar Differentialgeometrie

Simone Cecchini (Texas A&M)

Using index theory for twisted Dirac operators on Lipschitz bundles over non-compact manifolds, I will present Llarull-type comparison results in the setting of low-regularity scalar curvature geometry. The central analytic tool is a class of abstract cone operators, developed within a general functional analytic framework. As a first application, I will discuss spherical suspensions of odd-dimensional closed manifolds, establishing Lipschitz rigidity results that extend earlier work in even dimensions. As a second application, I will consider spin manifolds with cone-type singularities and Lipschitz comparison maps to spheres, proving scalar curvature rigidity in this singular and low-regularity context. This talk is based on joint work with Bernhard Hanke, Thomas Schick, and Lukas Schönlinner.