We show that closed manifolds supporting a nonpositively curved metric with negative -Ricci curvature, have positive simplicial volume. This answers a special case of a conjecture of Gromov. We also establish some related results concerning bounded cohomology and volume growth entropy for this new class of manifolds.
Cite this article
Chris Connell, Shi Wang, Positivity of simplicial volume for nonpositively curved manifolds with a Ricci-type curvature condition. Groups Geom. Dyn. 13 (2019), no. 3, pp. 1007–1034DOI 10.4171/GGD/512