Torsion Obstructions to Positive Scalar Curvature

TL;DR

This paper investigates how torsion in the fundamental group's homology obstructs positive scalar curvature metrics on manifolds, providing new examples of manifolds with such obstructions and their products.

Contribution

It introduces new torsion-based obstructions to positive scalar curvature and constructs manifolds illustrating these obstructions.

Findings

Torsion classes in homology obstruct positive scalar curvature.

Constructed manifolds without positive scalar curvature but with products that admit it.

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.