Pure braid groups are RFRS

Abstract

Agol in his 2014 ICM proceedings article \cite[Question 11]{Agol14} asks whether braid groups are (virtually) RFRS. We answer this positively by showing that pure braid groups are RFRS. As a consequence, several families of Artin groups are virtually RFRS, including those of type $A_n$ (the braid groups), $B_n=C_n$, ${\tilde{A}}_n$, and ${\tilde{C}}_n$. Our results also provide evidence toward the problem of whether braid groups, and more generally Artin groups, are virtually special; see \cite[Problem 9.4]{HagWi10}, \cite[Problem 13.4]{Wise14}.

13 pages. Comments welcome!