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Pré-Publication, Document De Travail Année : 2017

Multifraction reduction II: Conjectures for Artin-Tits groups

Résumé

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.
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Dates et versions

hal-01338095 , version 1 (27-06-2016)
hal-01338095 , version 2 (30-06-2016)
hal-01338095 , version 3 (30-01-2017)

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Patrick Dehornoy. Multifraction reduction II: Conjectures for Artin-Tits groups. 2017. ⟨hal-01338095v3⟩
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