BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Jason DeVito (The University of Tennessee at Martin) DTSTART:20230208T160000Z DTEND:20230208T170000Z DTSTAMP:20260423T021233Z UID:VSGS/65 DESCRIPTION:Title: Th e non-simply connected double soul conjecture\nby Jason DeVito (The Un iversity of Tennessee at Martin) as part of Virtual seminar on geometry wi th symmetries\n\n\nAbstract\nCheeger and Gromoll's Soul theorem asserts th at a complete non-compact Riemannian manifold of non-negative sectional cu rvature has the structure of a vector bundle over a closed totally geodesi c submanifold. The double soul conjecture (DSC) predicts an analogous str ucture on every closed simply connected Riemannian manifold of non-negativ e sectional curvature: it should decompose as a union of two disk bundles (possible of different ranks).\n\nIf one relaxes the hypothesis of the DS C to allow non-simply connected manifolds\, then previously only a single counterexample was known. We will discuss two new infinite families of co unterexamples\, one positively curved and the other flat. In addition\, a ll of our counterexamples are so-called biquotients\, quotients of Riemann ian homogeneous spaces by free isometric actions. We will also investiga te the biquotient structure on the flat examples\, finding that\, in contr ast with the homogeneous case\, they do not support a biquotient structure induced from a connected Lie group.\n LOCATION:https://researchseminars.org/talk/VSGS/65/ END:VEVENT END:VCALENDAR