Virtually cocompactly cubulated Artin-Tits groups

Abstract

We give a conjectural classification of virtually cocompactly cubulated Artin-Tits groups (i.e. having a finite index subgroup acting geometrically on a CAT(0) cube complex), which we prove for all Artin-Tits groups of spherical type, FC type or two-dimensional type. A particular case is that for $n\ge 4$, the $n$-strand braid group is not virtually cocompactly cubulated.

34 pages, 7 figures. Final journal version

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