Affiliation:
1. Department of Mathematics, University of British Columbia, Vancouver, BC Canada V6T 1Z2, Canada
Abstract
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.
Publisher
World Scientific Pub Co Pte Lt
Subject
Algebra and Number Theory
Cited by
3 articles.
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1. Ordering braids: In memory of Patrick Dehornoy;Journal of Knot Theory and Its Ramifications;2022-06-28
2. Isolated points in the space of left orderings of a group;Groups, Geometry, and Dynamics;2010
3. Discretely ordered groups;Algebra & Number Theory;2009-11-29