Nielsen-thurston Orderings and the Space of Braid Orderings
نویسندگان
چکیده
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.
منابع مشابه
ar X iv : m at h / 99 07 10 4 v 1 [ m at h . G T ] 1 5 Ju l 1 99 9 Orderings of mapping class groups after Thurston
We are concerned with mapping class groups of surfaces with nonempty boundary. We present a very natural method, due to Thurston, of finding many different left orderings of such groups. The construction involves equipping the surface with a hyperbolic structure, embedding the universal cover in the hyperbolic plane, and extending the action of the mapping class group on it to its limit points ...
متن کاملOn finite Thurston-type orderings of braid groups
We give an combinatorial description of a finite Thurston type ordering <T of the positive braid monoid B + n by introducing the C-normal form. The C-normal form can be seen as a generalization of Burckel’s normal form and Dehornoy’s Φ-normal form. Using this description, we determine the order type of well-ordered set (Bn, <T ) for all finite Thurston type orderings <T .
متن کاملFinite Thurston Type Orderings on Dual Braid Monoids
We give a combinatorial description of a finite Thurston type ordering < on the dual braid monoid B n by introducing the C-normal form and prove that the order-type of the well-ordered set (B n , <) is ωω n−2 . The C-normal form can be seen as a generalization of the rotating normal form defined by Fromentin and it is also a natural extension of C-normal form of the positive braid monoids defin...
متن کاملPreservation of Stochastic Orderings of Interdependent Series and Parallel Systems by Componentwise Switching to Exponentiated Models
This paper discusses the preservation of some stochastic orders between two interdependent series and parallel systems when the survival and distribution functions of all components switch to the exponentiated model. For the series systems, the likelihood ratio, hazard rate, usual, aging faster, aging intensity, convex transform, star, superadditive and dispersive orderings, and for the paralle...
متن کاملSome New Results on Stochastic Orderings between Generalized Order Statistics
In this paper we specify the conditions on the parameters of pairs of gOS’s under which the corresponding generalized order statistics are ordered according to usual stochastic ordering, hazard rate ordering, likelihood ratio ordering and dispersive ordering. We consider this problem in one-sample as well as two-sample problems. We show that some of the results obtained by Franco et al. ...
متن کامل