20.60 (2022)

We say that $G$ is a virtually compact special group if $G$ has a finite-index subgroup which is isomorphic to the fundamental group of a compact special complex (in the sense of F. Haglund, D. T. Wise, Geom. Funct. Anal., 17, no. 5 (2008), 1551–1620). Let $G$ be a virtual retract of a finitely generated right-angled Artin group. Must $G$ be a virtually compact special group?

An affirmative answer would provide an algebraic characterization of the class of virtually compact special groups as the class groups admitting finite index subgroups that are virtual retracts of right-angled Artin groups.