Left-orderable groups that don't act on the line
Dynamical Systems
2014-10-16 v2 Group Theory
Abstract
We show that the group of germs at infinity of orientation-preserving homeomorphisms of R admits no action on the line. This gives an example of a left-orderable group of the same cardinality as Homeo+(R) that does not embed in Homeo+(R). As an application of our techniques, we construct a finitely generated group of germs that does not extend to Homeo+(R) and, separately, extend a theorem of E. Militon on homomorphisms between groups of homeomorphisms.
Cite
@article{arxiv.1406.5575,
title = {Left-orderable groups that don't act on the line},
author = {Kathryn Mann},
journal= {arXiv preprint arXiv:1406.5575},
year = {2014}
}
Comments
13 pages. V2 contains corrections and improvements to section 4