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The Dehornoy order on braids. (L’ordre de Dehornoy sur les tresses.) (French) Zbl 1060.20033
Séminaire Bourbaki. Volume 1999/2000. Exposés 865–879. Paris: Société Mathématique de France. Astérisque 276, 7-28, Exp. No. 865 (2002).
Summary: 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.
For the entire collection see [Zbl 0981.00011].

MSC:
20F36 Braid groups; Artin groups
20F60 Ordered groups (group-theoretic aspects)
20F10 Word problems, other decision problems, connections with logic and automata (group-theoretic aspects)
57M07 Topological methods in group theory
06F15 Ordered groups
03E55 Large cardinals
08A50 Word problems (aspects of algebraic structures)
68Q70 Algebraic theory of languages and automata
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