2007/05/18 by Adam Clay, Clay, Adam, Dale Rolfsen +1
Mathematics · #20F36 #20F60 #Advanced Combinatorial Mathematics #Algebraic Topology (math.AT) #FOS: Mathematics #Geometric and Algebraic Topology #Group Theory (math.GR) #Homotopy and Cohomology in Algebraic Topology #math.AT #math.GR #msc:20F36 #msc:20F60
paper · pdf · doi:10.48550/arxiv.0705.2623
arxiv created 2007/05/18 · openalex publication_date 2007/05/18 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Dehornoy showed that the Artin braid groups Bn 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 Bn which is discretely ordered by the Dehornoy ordering.