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.
Publié le : 1999-07-05
Classification:
braid group,
ordered group,
set theory,
MSC 20F36, 20F60, 20F10, 57M07, 06F15, 03E55, 08A50, 68Q70,
[MATH.MATH-GR]Mathematics [math]/Group Theory [math.GR]
@article{hal-00124675,
author = {Kassel, Christian},
title = {L'ordre de Dehornoy sur les tresses},
journal = {HAL},
volume = {1999},
number = {0},
year = {1999},
language = {fr},
url = {http://dml.mathdoc.fr/item/hal-00124675}
}
Kassel, Christian. L'ordre de Dehornoy sur les tresses. HAL, Tome 1999 (1999) no. 0, . http://gdmltest.u-ga.fr/item/hal-00124675/