arXiv subjects
Publications and source records attributed to Alberto Casali.
We prove that the minimal volume entropy of mapping tori over oriented closed smooth $3$-manifolds vanishes. Our approach uses a variation of the amenable category and a suitable version of the minimal volume entropy of a homology class introduced by Babenko and Sabourau.
We provide an estimate of the amenable category of oriented closed connected complete affine manifolds whose fundamental group contains an infinite amenable normal subgroup. As an application we show that all such manifolds have zero simplicial volume. This answers a question by L\"uck in the case of complete affine manifolds. Our construction also provides the vanishing of stable integral simplicial volume and minimal volume entropy. This means that such manifolds satisfy integral approximation.