Positive scalar curvature on manifolds with odd order abelian fundamental groups

Hanke, Bernhard

doi:10.2140/gt.2021.25.497

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Positive scalar curvature on manifolds with odd order abelian fundamental groups

Bernhard Hanke

Geometry & Topology 25 (2021) 497–546

DOI: 10.2140/gt.2021.25.497

Abstract

We introduce Riemannian metrics of positive scalar curvature on manifolds with Baas–Sullivan singularities, prove a corresponding homology invariance principle and discuss admissible products.

Using this theory we construct positive scalar curvature metrics on closed smooth manifolds of dimension at least five which have odd order abelian fundamental groups, are nonspin and atoral. This solves the Gromov–Lawson–Rosenberg conjecture for a new class of manifolds with finite fundamental groups.

Keywords

manifolds with Baas–Sullivan singularities, positive scalar curvature, admissible products, group homology, Brown–Peterson homology

Mathematical Subject Classification 2010

Primary: 53C21, 57R15

Secondary: 55N20, 57T10

References

Publication

Received: 24 August 2019

Revised: 20 February 2020

Accepted: 21 March 2020

Published: 2 March 2021

Proposed: John Lott

Seconded: Dmitri Burago, Bruce Kleiner

Authors

Bernhard Hanke
Institut für Mathematik Universität Augsburg Augsburg Germany

Volume 25, issue 1 (2021)