Gromov's Conjecture on Positive Scalar Curvature and Simplicial Volume under a Fundamental Group Decay Property

Abstract

Gromov's simplicial volume is a fundamental invariant measuring the topological complexity of a manifold. A conjecture of Gromov predicts that every closed manifold admitting a metric of positive scalar curvature has vanishing simplicial volume. In this paper, we prove this conjecture under a natural weakening of the classical rapid decay (RD) property for the fundamental group.