The simplicial-volume conjecture for closed affine manifolds

Let $M$ be a closed affine manifold, and let $\|M\|$ denote its simplicial volume. Simplicial-volume conjecture. The simplicial volume of $M$ vanishes:

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

This is a stronger form of Chern's conjecture, motivated by the relation between simplicial volume and Euler characteristic. The paper proves the vanishing for the complete affine manifolds under its stated hypotheses, while the claim for arbitrary closed affine manifolds remains open.