Homological norms on nonpositively curved manifolds

Abstract

We relate the Gromov norm on homology classes to the harmonic norm on the dual cohomology and obtain double sided bounds in terms of the volume and other geometric quantities of the underlying manifold. Along the way, we provide comparisons to other related norms and quantities as well.

22 pages, minor changes, final version to appear in Comment. Math. Helv

References in corpus (2)

• Norms on the cohomology of hyperbolic 3-manifolds
• On splitting rank of non-compact type symmetric spaces and bounded cohomology