Left-orderable groups that don’t act on the line
نویسنده
چکیده
We show that the group G∞ 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 Γ ⊂ G∞ 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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