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

References in corpus (3)

• Proportionality principle for the simplicial volume of families of Q-rank 1 locally symmetric spaces
• Nonpositively curved manifolds containing a prescribed nonpositively curved hypersurface
• Relative Dehn functions of amalgamated products and HNN--extensions

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 $S{L}_n(\mathbb{R})$