Densely ordered braid subgroups

Details Densely ordered braid subgroups Densely ordered braid subgroups

2007-05-18

arxiv.org/abs/0705.2623v1

Mathematics

Group Theory

Scientific paper

Dehornoy showed that the Artin braid groups $B_n$ are left-orderable. This ordering is discrete, but we show that, for $n >2$ 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 $n$ for which the kernel is nontrivial). These results follow from a characterization of least positive elements of any normal subgroup of $B_n$ which is discretely ordered by the Dehornoy ordering.

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