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.
Cite this article
Patrick Dehornoy, Multifraction reduction II: Conjectures for Artin–Tits groups. J. Comb. Algebra 1 (2017), no. 3, pp. 229–287DOI 10.4171/JCA/1-3-1