Volume entropy semi-norm
Geometric Topology
2019-09-25 v1 Differential Geometry
Abstract
We introduce the volume entropy semi-norm in real homology and show that it satisfies functorial properties similar to the ones of the simplicial volume. Answering a question of M. Gromov, we prove that the volume entropy semi-norm is equivalent to the simplicial volume semi-norm in every dimension. We also establish a roughly optimal upper bound on the systolic volume of the multiples of any homology class.
Cite
@article{arxiv.1909.10803,
title = {Volume entropy semi-norm},
author = {Ivan Babenko and Stephane Sabourau},
journal= {arXiv preprint arXiv:1909.10803},
year = {2019}
}