The torsion-freeness conjecture for surface braid groups

Let $\Sigma\in {\bf Surf}$ be a marked surface and let $\Delta$ be a triangulation of $\Sigma$. Torsion-freeness conjecture. The group $Br_\Delta$ is torsion-free. The examples immediately preceding the conjecture include free groups and central elements, but no general torsion-freeness proof is supplied here.