Vanishing simplicial volume for certain affine manifolds
Geometric Topology
2018-02-13 v1
Abstract
We show that closed aspherical manifolds supporting an affine structure, whose holonomy map is injective and contains a pure translation, must have vanishing simplicial volume. This provides some further evidence for the veracity of the Auslander Conjecture. Along the way, we provide a simple cohomological criterion for aspherical manifolds with normal amenable subgroups of to have vanishing simplicial volume. This answers a special case of a question due to L\"uck.
Cite
@article{arxiv.1610.00832,
title = {Vanishing simplicial volume for certain affine manifolds},
author = {Michelle Bucher and Chris Connell and Jean-François Lafont},
journal= {arXiv preprint arXiv:1610.00832},
year = {2018}
}