Virtually nilpotent kernel conjecture for log canonical singularities

Let $(X,\Delta;x)$ be a log canonical singularity of dimension $n$. Let $\mathcal{D}(X,\Delta;X)$ denote the dual complex associated with the singularity, and consider the natural homomorphism from its regional fundamental group to the fundamental group of that dual complex. Define

$$N:=\operatorname{ker}\bigl(\pi_1(X,\Delta;x)\rightarrow \pi_1(\mathcal{D}(X,\Delta;X))\bigr).$$

Virtually nilpotent kernel conjecture. The normal subgroup $N$ is virtually nilpotent of rank at most $2n+1$.

This conjecture predicts stronger structure for the part of the fundamental group acting trivially on the dual complex. The surrounding discussion contrasts it with the possibility of arbitrary finitely presented groups for regional fundamental groups in dimension five; the asserted nilpotence bound remains open.