## EVENT DETAILS AND ABSTRACT

**Informal Geometric Analysis Seminar**
**Title:** Classifying sufficiently connected PSC manifolds in 4 and 5 dimensions

**Speaker:** Chao Li

**Speaker Info:** Princeton University

**Brief Description:**

**Special Note**: **Contact organizer for Zoom password**

**Abstract:**

In this talk, I will discuss some recent developments on the topology of closed manifolds admitting Riemannian metrics of positive scalar curvature. In particular, we will prove if a closed PSC manifold of dimension 4 (resp. 5) has vanishing $\pi_2$ (resp. vanishing $\pi_2$ and $\pi_3$), then a finite cover of it is homotopy equivalent to $S^n$ or connected sums of $S^{n-1}\times S^1$. This extends a previous theorem on the non-existence of Riemannian metrics of positive scalar curvature on aspherical manifolds in 4 and 5 dimensions, due to Chodosh and myself and independently Gromov. A key step in the proof is a homological filling estimate in sufficiently connected PSC manifolds. This talk is based on joint work with Otis Chodosh and Yevgeny Liokumovich.

**Date:** Thursday, May 27, 2021

**Time:** 04:00pm

**Where:** Zoom: 963 4867 1534

**Contact Person:** Ben Weinkove

**Contact email:** weinkove@math.northwestern.edu

**Contact Phone:**

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