Densely ordered braid subgroups
Group Theory
2007-05-23 v1 Algebraic Topology
Abstract
Dehornoy showed that the Artin braid groups are left-orderable. This ordering is discrete, but we show that, for the Dehornoy ordering, when restricted to certain natural subgroups, becomes a dense ordering. Among subgroups which arise are the commutator subgroup and the kernel of the Burau representation (for those for which the kernel is nontrivial). These results follow from a characterization of least positive elements of any normal subgroup of which is discretely ordered by the Dehornoy ordering.
Cite
@article{arxiv.0705.2623,
title = {Densely ordered braid subgroups},
author = {Adam Clay and Dale Rolfsen},
journal= {arXiv preprint arXiv:0705.2623},
year = {2007}
}