Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 20 (2024), 069, 22 pages      arXiv:2112.04825      https://doi.org/10.3842/SIGMA.2024.069
Contribution to the Special Issue on Global Analysis on Manifolds in honor of Christian Bär for his 60th birthday

Torsion Obstructions to Positive Scalar Curvature

Misha Gromov ab and Bernhard Hanke c
a) Institut des Hautes Études Scientifiques, 91893 Bures-sur-Yvette, France
b) Courant Institute of Mathematical Sciences, New York University, New York, NY 10012-1185, USA
c) Institut für Mathematik, University of Augsburg, 86135 Augsburg, Germany

Received November 07, 2023, in final form July 17, 2024; Published online July 30, 2024

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.

Key words: positive scalar curvature; toral manifold; enlargeability; $\mu$-bubble; group homology; Riemannian foliation; band width inequality.

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