On spaces of Conradian group orderings
Group Theory
2010-03-31 v2 Dynamical Systems
Abstract
We classify -orderable groups admitting only finitely many -orderings. We show that if a -orderable group has infinitely many -orderings, then it actually has uncountably many -orderings, and none of these is isolated in the space of -orderings. As a relevant example, we carefully study the case of Baumslag-Solitar's group B(1,2). We show that B(1,2) has four -orderings, each of which is bi-invariant, but its space of left-orderings is homeomorphic to the Cantor set.
Keywords
Cite
@article{arxiv.0907.4340,
title = {On spaces of Conradian group orderings},
author = {Cristóbal Rivas},
journal= {arXiv preprint arXiv:0907.4340},
year = {2010}
}