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Videos Year : 2021

Classifying sufficiently connected PSC manifolds in 4 and 5 dimensions

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Chao Li
  • Function : Author
Fanny Bastien
Hugo Béchet
  • Function : Producer

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 π2 (resp. vanishing π2 and π3), then a finite cover of it is homotopy equivalent to Snor connected sums of Sn-1 x S1. 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 is based on joint work with Otis Chodosh and Yevgeny Liokumovich.

Dates and versions

hal-03711602 , version 1 (01-07-2022)

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Attribution - NonCommercial - NoDerivatives

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  • HAL Id : hal-03711602 , version 1

Cite

Chao Li, Fanny Bastien, Hugo Béchet. Classifying sufficiently connected PSC manifolds in 4 and 5 dimensions: Summer School 2021 - Curvature Constraints and Spaces of Metrics. 2021. ⟨hal-03711602⟩
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