Left-orderable groups that don't act on the line

2014/06/21 by Kathryn Mann, Mann, Kathryn · 1 citation
Mathematics · #Dynamical Systems (math.DS) #FOS: Mathematics #Group Theory (math.GR) #math.DS #math.GR

paper · pdf · doi:10.48550/arxiv.1406.5575

13 pages. V2 contains corrections and improvements to section 4

arxiv created 2014/10/15 · arxiv updated 2014/10/16

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.

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