Download this article
 Download this article For screen
For printing
Recent Issues

Volume 28
Issue 2, 497–1003
Issue 1, 1–496

Volume 27, 9 issues

Volume 26, 8 issues

Volume 25, 7 issues

Volume 24, 7 issues

Volume 23, 7 issues

Volume 22, 7 issues

Volume 21, 6 issues

Volume 20, 6 issues

Volume 19, 6 issues

Volume 18, 5 issues

Volume 17, 5 issues

Volume 16, 4 issues

Volume 15, 4 issues

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 5 issues

Volume 11, 4 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 3 issues

Volume 7, 2 issues

Volume 6, 2 issues

Volume 5, 2 issues

Volume 4, 1 issue

Volume 3, 1 issue

Volume 2, 1 issue

Volume 1, 1 issue

The Journal
About the Journal
Editorial Board
Editorial Procedure
Subscriptions
 
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
 
ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Author Index
To Appear
 
Other MSP Journals
Classifying sufficiently connected PSC manifolds in $4$ and $5$ dimensions

Otis Chodosh, Chao Li and Yevgeny Liokumovich

Geometry & Topology 27 (2023) 1635–1655
Abstract

We show that if N is a closed manifold of dimension n = 4 (resp. n = 5) with π2(N) = 0 (resp. π2(N) = π3(N) = 0) that admits a metric of positive scalar curvature, then a finite cover N^ of N is homotopy equivalent to Sn or connected sums of Sn1 × S1. Our approach combines recent advances in the study of positive scalar curvature with a novel argument of Alpert, Balitskiy and Guth.

Additionally, we prove a more general mapping version of this result. In particular, this implies that if N is a closed manifold of dimensions 4 or 5, and N admits a map of nonzero degree to a closed aspherical manifold, then N does not admit any Riemannian metric with positive scalar curvature.

Keywords
positive scalar curvature, Urysohn width, minimal surfaces, $\mu$–bubbles
Mathematical Subject Classification
Primary: 53C21
References
Publication
Received: 21 June 2021
Revised: 13 September 2021
Accepted: 15 October 2021
Published: 15 June 2023
Proposed: John Lott
Seconded: Urs Lang, Gang Tian
Authors
Otis Chodosh
Department of Mathematics
Stanford University
Stanford, CA
United States
Chao Li
Courant Institute of Mathematical Sciences
New York University
New York, NY
United States
Yevgeny Liokumovich
Department of Mathematics
University of Toronto
Toronto ON
Canada

Open Access made possible by participating institutions via Subscribe to Open.