Tits Alternative for -dimensional complexes

Abstract

We prove the Tits Alternative for groups acting on $2$ -dimensional $\mathrm {CAT}(0)$ complexes with a bound on the order of the cell stabilisers.

Intersection of parabolic subgroups in even Artin groups of FC-type

“…For Artin-Tits groups of FC-type, this dichotomy (the original for Tits) was proved by A. Martin and P. Przytycki [21]. For 2-dimensional Artin groups, there are alternatives that restrict the classes of virtually solvable groups that can appear as subgroups [23,22] to only Z, Z 2 and K in certain cases. The full Tits alternative for 2-dimensional Artin groups was settled by A.…”