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Article Dans Une Revue Compositio Mathematica Année : 2014

Coherent presentations of Artin monoids

Résumé

We compute coherent presentations of Artin monoids, that is presentations by generators, relations, and relations between the relations. For that, we use methods of higher-dimensional rewriting that extend Squier's and Knuth-Bendix's completions into a homotopical completion-reduction, applied to Artin's and Garside's presentations. The main result of the paper states that the so-called Tits-Zamolodchikov 3-cells extend Artin's presentation into a coherent presentation. As a byproduct, we give a new constructive proof of a theorem of Deligne on the actions of an Artin monoid on a category.
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Dates et versions

hal-00682233 , version 1 (23-03-2012)
hal-00682233 , version 2 (14-03-2013)
hal-00682233 , version 3 (07-07-2014)
hal-00682233 , version 4 (22-05-2015)

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Stéphane Gaussent, Yves Guiraud, Philippe Malbos. Coherent presentations of Artin monoids. Compositio Mathematica, 2014, pp.1-42. ⟨10.1112/S0010437X14007842⟩. ⟨hal-00682233v3⟩
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