Kassel, Christian 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]. Cited in 1 Document 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 Keywords:braid groups; ordered groups; mapping class groups; word problem; large cardinals; selfdistributivity PDFBibTeX XMLCite \textit{C. Kassel}, Astérisque 276, 7--28, Exp. No. 865 (2002; Zbl 1060.20033) Full Text: Numdam EuDML