Free orbits for minimal actions on the circle

Brum, Joaquín; Martínez, Matilde; Potrie, Rafael

doi:10.1090/proc/13698

Free orbits for minimal actions on the circle
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by Joaquín Brum, Matilde Martínez and Rafael Potrie PDF

Proc. Amer. Math. Soc. 146 (2018), 581-587 Request permission

Abstract:

We prove that if $\Gamma$ is a countable group without a subgroup isomorphic to $\mathbb {Z}^2$ that acts faithfully and minimally by orientation-preserving homeomorphisms on the circle, then it has a free orbit. We give examples showing that this does not hold for actions by homeomorphisms of the line.

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