2009/06/15 by Andrés Navas, Andres Navas, Navas, Andres +2 · 1 citation
Computer Science · Mathematics · #06F15 #20F36 #20F60 #FOS: Mathematics #Group Theory (math.GR) #Markov Chains and Monte Carlo Methods #Mathematical Dynamics and Fractals #Topological and Geometric Data Analysis #math.GR #msc:06F15 #msc:20F36 #msc:20F60
paper · pdf · doi:10.48550/arxiv.0906.2605
arxiv created 2009/06/15 · openalex publication_date 2009/06/15 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study the topological space of left-orderings of the braid group, and its subspace of Nielsen-Thurston orderings. Our main result is that no Nielsen-Thurston ordering is isolated in the space of braid orderings. In the course of the proof, we classify the convex subgroups and calculate the Conradian soul for any Nielsen-Thurston ordering of Bn. We also prove that for a large class of Nielsen-Thurston orderings, including all those of infinite type, a stronger result holds: they are approximated by their own conjugates. On the other hand, we suggest an example of a Nielsen-Thurston ordering which may not be approximated by its conjugates.