Positivity of simplicial volume for nonpositively curved manifolds with a Ricci-type curvature condition

  • Chris Connell

    Indiana University, Bloomington, USA
  • Shi Wang

    Indiana University, Bloomington, USA
Positivity of simplicial volume for nonpositively curved manifolds with a Ricci-type curvature condition cover
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Abstract

We show that closed manifolds supporting a nonpositively curved metric with negative (n4+1)(\lfloor \frac{n}{4}\rfloor+1)-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. 1007–1034

DOI 10.4171/GGD/512