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Topology, Algebraic Geometry, and Dynamics Seminar (TADS): Nonnegative curvature on bundles over smooth homotopy 7-spheres

Oct 3, 2025, 1:30 - 2:30 PM

 

Speaker: David Duncan, James Madison University

Title: Nonnegative curvature on bundles over smooth homotopy 7-spheres
 

Abstract: Motivated by the famous Soul Theorem, the Inverse Soul Problem asks: For a given closed manifold M with nonnegative (sectional) curvature, which vector bundles over M admit a complete metric of nonnegative curvature? A result of Goette-Kerin-Shankar says that all smooth homotopy 7-spheres admit nonnegative curvature metrics, thereby making these good candidates for M. In this talk, I will describe joint work with Ravi Shankar and Rebecca Field in which we show that every vector bundle over every smooth homotopy 7-sphere admits a complete nonnegative curvature metric. This resolves a 25-year-old question by Grove and Ziller.

 

Date/Time: Friday October 3, 1:30pm

Location: Exploratory Hall, Room 4208

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