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DENSELY ORDERED BRAID SUBGROUPS

ADAM CLAY

Department of Mathematics, University of British Columbia, Vancouver, BC Canada V6T 1Z2, Canada

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and

DALE ROLFSEN

Department of Mathematics, University of British Columbia, Vancouver, BC Canada V6T 1Z2, Canada

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https://doi.org/10.1142/S0218216507005543Cited by:2 (Source: Crossref)

Abstract

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.

Dedicated to Louis H. Kauffman on his 60th birthday

Keywords:

AMSC: 20F36, 20F60, 06F15

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