Multifraction reduction. II: Conjectures for Artin-Tits groups (Q2405875)

Summary: Multifraction reduction is a new approach to the word problem for Artin-Tits groups and, more generally, for the enveloping group of a monoid in which any two elements admit a greatest common divisor. This approach is based on a rewrite system (``reduction'') that extends free group reduction. In this paper, we show that assuming that reduction satisfies a weak form of convergence called semi-convergence is sufficient for solving the word problem for the enveloping group, and we connect semi-convergence with other conditions involving reduction. We conjecture that these properties are valid for all Artin-Tits monoids, and provide partial results and numerical evidence supporting such conjectures. For Part I see [the author, ibid. 1, No. 2, 185--228 (2017; Zbl 1422.20020)].