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

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Hanke, Bernhard
Max Planck Institute for Mathematics, Max Planck Society;

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https://doi.org/10.2140/gt.2021.25.497
(Publisher version)

https://doi.org/10.48550/arXiv.1908.00944
(Preprint)

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Hanke_Positive scalar curvature on manifolds with odd order abelian fundamental groups_2021.pdf
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Citation

Hanke, B. (2021). Positive scalar curvature on manifolds with odd order abelian fundamental groups. Geometry & Topology, 25(1), 497-546. doi:10.2140/gt.2021.25.497.

Cite as: https://hdl.handle.net/21.11116/0000-0008-AF1B-6

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.