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Geometric Analysis Seminar

On a generalization of Geroch's conjecture

Sven Hirsch

Location:  Hill-705
Date & time: Tuesday, 02 April 2024 at 2:50PM - 3:50PM

Abstract: The theorem of Bonnet-Myers implies that manifolds with topology \(M^{n-1}times S^1\) do not admit a metric of positive Ricci curvature, while the resolution of Geroch's conjecture shows that the torus \(T^n\) does not admit a metric of positive scalar curvature. In this talk I will introduce a new notion of curvature which interpolates between Ricci and scalar curvature (so-called \(m\)-intermediate curvature) and use stable weighted slicings to show that for \(nle7\) the manifolds \(M^{n-m}times T^m\) do not admit a metric of positive \(m\)-intermediate curvature. This is joint work with Simon Brendle and Florian Johne.

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