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Scalar curvature on manifolds with at least two ends

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If you have a question about this talk, please contact Oscar Randal-Williams.

We will discuss geometric and topological consequences of positive lower scalar curvature bounds on manifolds with at least two ends. This will include two aspects: One the one hand, quantitative distance estimates in the presence of a particular lower scalar curvature bound, and on the other hand, qualitative obstructions to the existence of complete positive scalar curvature metrics on certain (non-compact) manifolds. Both types of results rely on augmenting classical techniques to study scalar curvature – Dirac operator and minimal hypersurface methods – via a certain potential function. They are motivated by recent questions of Gromov and an earlier conjecture due to Rosenberg—Stolz. The talk will in part be based on joint work with Simone Cecchini and Daniel Räde.

This talk is part of the Differential Geometry and Topology Seminar series.

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