Minimal volume entropy of free-by-cyclic groups and 2-dimensional right-angled Artin groups

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Let G be a free-by-cyclic group or a 2-dimensional right-angled Artin group. We provide an algebraic and a geometric characterization for when each aspherical simplicial complex with fundamental group isomorphic to G has minimal volume entropy equal to 0. In the nonvanishing case, we provide a positive lower bound to the minimal volume entropy of an aspherical simplicial complex of minimal dimension for these two classes of groups. Our results rely upon a criterion for the vanishing of the minimal volume entropy for 2-dimensional groups with uniform uniform exponential growth. This criterion is shown by analyzing the fiber \(\pi _1\)-growth collapse and non-collapsing assumptions of Babenko–Sabourau (Minimal volume entropy and fiber growth, arXiv:2102.04551, 2020).