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

Abstract

We show that closed manifolds supporting a nonpositively curved metric with negative $([\frac{n}{4}]+1)$-Ricci curvature, have positive simplicial volume. This answers a special case of a conjecture of Gromov.

24 pages, Minor revisions, final version to appear in Groups Geom. Dyn

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Cited by in corpus (6)

• Amenable category and complexity
• Some remarks on the simplicial volume of nonpositively curved manifolds
• On the simplicial volume and the Euler characteristic of (aspherical) manifolds
• Topological volumes of fibrations: A note on open covers
• Steenrod problem and the domination relation
• Geometric cycles and bounded cohomology for a cocompact lattice in $S{L}_n(\mathbb{R})$