Automorphisms acting on the left-orderings of a bi-orderable group
Group Theory
2016-10-25 v1
Abstract
We generalize a result of T. Koberda by showing that the natural action of the automorphism group on the space of left-orderings is faithful for all nonabelian bi-orderable groups G, as well as for a certain class of left-orderable groups that includes the braid groups. As a corollary we show that the action of the automorphism group of G on the boundary of G is faithful whenever G is bi-orderable and hyperbolic. We also analyze the action of the commensurator of G on its space of virtual left-orderings.
Keywords
Cite
@article{arxiv.1610.07223,
title = {Automorphisms acting on the left-orderings of a bi-orderable group},
author = {Adam Clay and Sina Zabanfahm},
journal= {arXiv preprint arXiv:1610.07223},
year = {2016}
}
Comments
12 pages, no figures