Vanishing simplicial volume conjecture for affine manifolds

Let $M$ be a closed manifold supporting an affine structure, meaning that it admits an atlas whose transition maps are affine transformations. For a closed oriented manifold, write $||M||$ for its simplicial volume.

Vanishing simplicial volume conjecture. If $M$ is a closed manifold supporting an affine structure, then

$$||M||=0.$$

The paper proves this when $M$ is aspherical and its affine holonomy representation is injective with non-trivial translational subgroup. It also proves the claim for complete affine manifolds whose holonomy contains a pure translation; the general case remains open. In the complete setting, the Auslander conjecture predicts that the fundamental group is virtually polycyclic.