Squier's intersection conjecture for braid-group power subgroups

Let $B_n$ be the braid group on $n$ strands, and for each positive integer $k$ let $B_n[k]$ be the normal subgroup generated by $g_j^k$ for $1\leq j\leq n-1$. Squier's intersection conjecture. The intersection of these subgroups is trivial:

$$\bigcap_k B_n[k]=\{1\}.$$

The paper states a theorem proving this conjecture using the asymptotic faithfulness of quantum representations of mapping class groups. Thus the conjecture is resolved.