Virtual specialness of braid and Artin groups

Determine whether braid groups, and more generally all Artin groups, are virtually special.

Background

The paper proves that pure braid groups are RFRS and derives virtual RFRS results for several families of Artin groups. Since virtually special groups are virtually RFRS, these results provide indirect evidence relevant to the stronger virtual-specialness problem. The cited formulations concern both braid groups and the broader class of Artin groups, but the paper does not resolve virtual specialness.

References

Our results also provide evidence toward the problem of whether braid groups, and more generally Artin groups, are virtually special; see Problem 9.4, Problem 13.4.

Pure braid groups are RFRS  (2608.13978 - Wu et al., 14 Aug 2026) in Abstract; Introduction