Rewriting systems in sufficiently large Artin-Tits groups
Eddy GODELLE and Sarah REES
Keywords
word problem, rewriting, Artin groups, Artin-Tits groups, large type
Status
Published in J. Alg. 466 (2016) 284--307.
Abstract
A conjecture of Dehornoy claims that, given a presentation of an Artin-Tits group, every word that represents the identity can be transformed into the trivial word
using the braid relations, together with certain rules
(between pairs of words that are not both positive)
that can be derived directly from the braid relations, as well as free
reduction, but
without introducing trivial factors $ss^{-1} $ or $s^{-1} s$. This conjecture
is known to be true for Artin-Tits groups of spherical type or of FC type. We prove the conjecture for Artin-Tits groups of sufficiently large type.
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