Virtually cocompactly cubulated Artin-Tits groups
Résumé
We give a complete classification of virtually cocompactly cubulated Artin-Tits groups (i.e. having a finite index subgroup acting geometrically on a CAT(0) cube complex). A particular case is that for n≥4, the n-strand braid group is not virtually cocompactly cubulated. The methods extend to give a classification of virtually cocompactly cubulated groups among mapping class group of surfaces and (outer) automorphism groups of free groups.