Torsion Obstructions to Positive Scalar Curvature - Gromov, Misha; Hanke, Bernhard (Symmetry, Integrability and Geometry: Methods and Applications, 2024)
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 that do not admit positive scalar curvature metrics, but whose Cartesian products admit such metrics.