Nielsen-Thurston orderings and the space of braid orderings

Andres Navas (1) , Bert Wiest (2)

1 UCHILE - Universidad de Chile = University of Chile [Santiago]
2 IRMAR - Institut de Recherche Mathématique de Rennes

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 B_n. 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.

Domaines: Théorie des groupes [math.GR]

Andres Navas, Bert Wiest. Nielsen-Thurston orderings and the space of braid orderings. Bulletin of the London Mathematical Society, 2011, 43 (5), pp.901-911. ⟨10.1112/blms/bdr027⟩. ⟨hal-00395102⟩