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Free orbits for minimal actions on the circle


Authors: Joaquín Brum, Matilde Martínez and Rafael Potrie
Journal: Proc. Amer. Math. Soc.
MSC (2010): Primary 37B05; Secondary 20F38, 20F65
DOI: https://doi.org/10.1090/proc/13698
Published electronically: October 12, 2017
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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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Additional Information

Joaquín Brum
Affiliation: IMERL, Facultad de Ingeniería, Universidad de la República, 2400 9201 Montevideo, Uruguay
Email: joaquinbrum@fing.edu.uy

Matilde Martínez
Affiliation: IMERL, Facultad de Ingeniería,Universidad de la República, 2400 9201 Montevideo, Uruguay
Email: matildem@fing.edu.uy

Rafael Potrie
Affiliation: CMAT, Facultad de Ciencias, Universidad de la República, 11400 Montevideo, Uru- guay
Email: rpotrie@cmat.edu.uy

DOI: https://doi.org/10.1090/proc/13698
Received by editor(s): September 29, 2016
Received by editor(s) in revised form: February 12, 2017
Published electronically: October 12, 2017
Additional Notes: The authors were partially supported by CSIC grupo 618.
Communicated by: Nimish Shah
Article copyright: © Copyright 2017 American Mathematical Society