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Symmetry, Integrability and Geometry: Methods and Applications, 2024, Volume 20, 069, 22 pp.
DOI: https://doi.org/10.3842/SIGMA.2024.069 (Mi sigma2071) 		 
Torsion Obstructions to Positive Scalar Curvature

Misha Gromovab, Bernhard Hankec

a Courant Institute of Mathematical Sciences, New York University, New York, NY 10012-1185, USA
b Institut des Hautes Études Scientifiques, 91893 Bures-sur-Yvette, France
c Institut für Mathematik, University of Augsburg, 86135 Augsburg, Germany
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DOI: https://doi.org/10.3842/SIGMA.2024.069
Abstract: We study obstructions to the existence of Riemannian metrics of positive scalar curvature on closed smooth manifolds arising from torsion classes in the integral homology of their fundamental groups. As an application, we construct new examples of manifolds which do not admit positive scalar curvature metrics, but whose Cartesian products admit such metrics.
Keywords: positive scalar curvature, toral manifold, enlargeability, $\mu$-bubble; group homology, Riemannian foliation, band width inequality.
Funding agency Grant number
Deutsche Forschungsgemeinschaft
B.H. acknowledges support from NYU, the IAS Princeton and the DFG-funded Special Priority Program 2026 Geometry at Infinity.
Received: November 7, 2023; in final form July 17, 2024; Published online July 30, 2024
Document Type: Article
MSC: 53C21, 53C23, 20J06, 53C12, 55N10
Language: English
Citation: Misha Gromov, Bernhard Hanke, “Torsion Obstructions to Positive Scalar Curvature”, SIGMA, 20 (2024), 069, 22 pp.
Citation in format AMSBIB
\Bibitem{GroHan24}
\by Misha~Gromov, Bernhard~Hanke
\paper Torsion Obstructions to Positive Scalar Curvature
\jour SIGMA
\yr 2024
\vol 20
\papernumber 069
\totalpages 22
\mathnet{http://mi.mathnet.ru/sigma2071}
\crossref{https://doi.org/10.3842/SIGMA.2024.069}
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