Some remarks on the simplicial volume of nonpositively curved manifolds

Abstract

We show that any closed manifold with a metric of nonpositive curvature that admits either a single point rank condition or a single point curvature condition has positive simplicial volume. We use this to provide a differential geometric proof of a conjecture of Gromov in dimension three.

14 pages, 1 figure. Minor revisions

References in corpus (1)

• Positivity of Simplicial Volume for Nonpositively Curved Manifolds with a Ricci-type curvature condition

Cited by in corpus (2)

• On the simplicial volume and the Euler characteristic of (aspherical) manifolds
• Simplicial volume of one-relator groups and stable commutator length