THE TITS CONJECTURE FOR LOCALLY REDUCIBLE ARTIN GROUPS

Abstract

Given an Artin system (A,S), a conjecture of Tits states that the subgroup A(2) of A generated by the squares of the generators in S is subject only to the obvious commutator relations between generators. In particular, A(2) is a right-angled Artin group. We prove this conjecture for a class of infinite type Artin groups, called locally reducible Artin groups, for which the associated Deligne complex has a CAT(0) geometry. We also prove that for any special subgroup AT of A, A(2)∩AT=(AT)(2).