The solution to a conjecture of Tits on the subgroup generated by the squares of the generators of an Artin group

Abstract

It was conjectured by Tits that the only relations amongst the squares of the standard generators of an Artin group are the obvious ones, namely that a^2 and b^2 commute if ab=ba appears as one of the Artin relations. In this paper we prove Tits' conjecture for all Artin groups. More generally, we show that, given a number m(s)>1 for each Artin generator s, the only relations amongst the powers s^m(s) of the generators are that a^m(a) and b^m(b) commute if ab=ba appears amongst the Artin relations.

18 pages, 11 figures (.eps files generated by pstricks.tex). Prepublication du Laboratoire de Topologie UMR 5584 du CNRS (Univ. de Bourgogne)