Topological Zimmer conjecture for low-dimensional closed aspherical manifolds

Let $n\geq 3$, and let $M^r$ be a closed aspherical $r$-manifold, meaning that its universal cover is contractible, with $r<n$. A group action of $\mathrm{SL}_{n}(\mathbb{Z})$ on $M$ by homeomorphisms is a homomorphism

$$\mathrm{SL}_{n}(\mathbb{Z})\longrightarrow \operatorname{Homeo}(M).$$

Topological Zimmer conjecture for closed aspherical manifolds. Every such action factors through a finite group.

This is a proposed extension of the low-dimensional topological Zimmer statement from general compact manifolds to closed aspherical manifolds. The supplied text does not state a resolution or give a status beyond its presentation as a conjecture.