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Topology/Geometry Seminar

Ricci limit spaces are semi-locally simply connected

Jikang Wang (Rutgers University)

Location:  Zoom
Date & time: Tuesday, 30 November 2021 at 11:15AM - 12:15PM

Abstract: In this talk, we will discuss local topology of a Ricci limit space \((X,p)\), which is the pointed Gromov-Hausdorff limit of a sequence of complete \(n\)-manifolds with a uniform Ricci curvature lower bound. I will show that \((X,p)\) is semi-locally simply connected, that is, for any point \(x \in X\), we can find a small ball \(B_r(x)\) such that any loop in \(B_r(x)\) is contractible in \(X\). We will also discuss a slice theorem for pseudo-group actions on the Ricci limit space and how to use this slice theorem to construct a homotopy map on the limit space. Partial of this material is joint work with Jiayin Pan.

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