Minimal volume entropy and fiber growth
Year: 2025
Type: article
Abstract: This article deals with topological assumptions under which the minimal volume entropy of a closed manifold M , and more generally of a finite simplicial complex X , vanishes or is positive. These topological conditions are expressed in terms of the growth of the fundamental group of the fibers of maps from a given finite simplicial complex X to lower dimensional simplicial complexes P . This leads to a complete characterization of spaces with positive minimal volume entropy for finite simplicial complexes whose fundamental group has uniform exponential growth with no subgroup of intermediate growth. As pointed out to us by Vitali Kapovitch, these conditions are related to collapsing with Ricci curvature bounded below and lead to a refinement of Gromov’s isolation theorem. We also give examples of finite simplicial complexes with zero simplicial volume and arbitrarily large minimal volume entropy.
DOI: 10.5802/jep.295
Authors: Ivan Babenko, Stéphane Sabourau
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4408890741