I recall that Thurston answered a question, showing that a particular graph braid group is the fundamental group of a three-manifold. I even recall that the answer proved that the three-manifold was arithmetic. I told all this to a student, and now, embarrassingly, I can't find the question or the answer. I suspect that the question poser has deleted their account. I've emailed the poser and not gotten a reply... so - is there some way for me to find this answer? I'd be happy to see just the answer and not the question (if that is needed to protect the question poser's wishes).