English

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 π1\pi_1 to have vanishing simplicial volume. This answers a special case of a question due to L\"uck.

Keywords

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}
}
R2 v1 2026-06-22T16:09:37.795Z