Speaker: Dr. David Duncan (James Madison University)
Location: Hamilton Hall, Room 312
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.
