Speaker: Thunwa Theerakarn, UC Riverside
Title: Locally volume collapsed 4-manifolds with respect to a lower sectional curvature bound
Abstract:Perelman stated without proof that a 3-dimensional compact Riemannian manifold which is locally volume collapsed, with respect to a lower curvature bound, is a graph manifold. The theorem was used to complete his Ricci flow proof of Thurston's geometrization conjecture. Kleiner and Lott gave a proof of the theorem as a part of their presentation of Perelman's proof.In this talk, I will present a generalization of Perelman's local collapsing theorem to 4-dimensional closed Riemannian manifolds. Namely, under some regularity assumptions, if a 4-dimensional closed Riemannian manifold is locally volume collapsed then it admits an $F$-structure or a metric of nonnegative sectional curvature.
Friday, November 30 at 11:10am to 12:00pm
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