Volume 25, issue 1 (2021)

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Positive scalar curvature on manifolds with odd order abelian fundamental groups

Bernhard Hanke

Geometry & Topology 25 (2021) 497–546

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.

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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
Received: 24 August 2019
Revised: 20 February 2020
Accepted: 21 March 2020
Published: 2 March 2021
Proposed: John Lott
Seconded: Dmitri Burago, Bruce Kleiner
Bernhard Hanke
Institut für Mathematik
Universität Augsburg