L'ordre de Dehornoy sur les tresses

Christian Kassel (1)

1 IRMA - Institut de Recherche Mathématique Avancée

At the beginning of the 1990's Dehornoy, investigating selfdistributive systems, constructed a linear order on Artin's braid groups. Selfdistributive systems are sets equipped with a binary law satisfying the identity x(yz) = (xy)(xz). Such systems came up in the study of a large cardinal axiom in set theory. In this text we present Dehornoy's work and its unexpected link with set theory. We also survey two recent geometric constructions of Dehornoy's order.

Mots clés: braid group; ordered group; set theory

Domaines: Théorie des groupes [math.GR]

Christian Kassel. L'ordre de Dehornoy sur les tresses. Séminaire Bourbaki (novembre 1999), 1999, Paris, France. pp.7-28. ⟨hal-00124675⟩