Conférence

C. Li - Classifying sufficiently connected PSC manifolds in 4 and 5 dimensions

Réalisation : 30 juin 2021 Mise en ligne : 30 juin 2021
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Descriptif

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.

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Notice
Langue :
Anglais
Crédits
Fanny Bastien (Réalisation), Hugo BÉCHET (Réalisation)
Conditions d'utilisation
CC BY-NC-ND 4.0
Citer cette ressource:
I_Fourier. (2021, 30 juin). C. Li - Classifying sufficiently connected PSC manifolds in 4 and 5 dimensions. [Vidéo]. Canal-U. https://www.canal-u.tv/107571. (Consultée le 21 mai 2022)
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