A conjecture about Artin-Tits groups

We conjecture that the word problem of Artin-Tits groups can be solved without introducing trivial factors ss(-1) or s(-1)s. Here we make this statement precise and explain how it can be seen as a weak form of hyperbolicity. We prove the conjecture in the case of Artin-Tits groups of type FC, and we discuss various possible approaches for further extensions, in particular a syntactic argument that works at least in the right-angled case. (C) 2012 Elsevier B.V. All rights reserved.