Minimal volume entropy and fiber growth

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 $P$. We also give examples of finite simplicial complexes with zero simplicial volume and arbitrarily large minimal volume entropy.

Extended version. A statement was modified and a proof was corrected. arXiv admin note: text overlap with arXiv:2002.11069