Lück's torsion-growth conjecture for residually finite aspherical manifolds

Let $M^n$ be a closed aspherical $n$-manifold with residually finite fundamental group. Let $\Gamma_k\vartriangleleft\pi_1(M^n)$ be any normal chain with $\bigcap_k\Gamma_k=1$. Lück's conjecture. If $i\ne(n-1)/2$, then

$$\limsup\frac{\log\lvert H_i(B\Gamma_k;\mathbb{Z})_{tors}\rvert}{[\pi_1(M^n):\Gamma_k]}=0.$$

This proposes a general torsion-growth vanishing principle beyond arithmetic locally symmetric spaces and is presented as a conjectural consequence motivated by the Bergeron–Venkatesh conjecture. Its status is open.