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Short proofs of theorems of Malyutin and Margulis


Author: Eli Glasner
Journal: Proc. Amer. Math. Soc. 145 (2017), 5463-5467
MSC (2010): Primary 54H20, 37B05, 20B07
DOI: https://doi.org/10.1090/proc/13664
Published electronically: July 10, 2017
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Abstract: The Ghys-Margulis alternative asserts that a subgroup $ G$ of homeomorphisms of the circle which does not contain a free subgroup on two generators must admit an invariant probability measure. Malyutin's theorem classifies minimal actions of $ G$. We present a short proof of Malyutin's theorem and then deduce Margulis' theorem which confirms the G-M alternative. The basic ideas are borrowed from the original work of Malyutin, but our proof is considerably shorter.


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Additional Information

Eli Glasner
Affiliation: Department of Mathematics, Tel Aviv University, 69978 Tel Aviv, Israel
Email: glasner@math.tau.ac.il

DOI: https://doi.org/10.1090/proc/13664
Received by editor(s): June 28, 2016
Received by editor(s) in revised form: January 11, 2017, January 12, 2017, and January 17, 2017
Published electronically: July 10, 2017
Additional Notes: This research was supported by a grant of the Israel Science Foundation (ISF 668/13)
Communicated by: Nimish Shah
Article copyright: © Copyright 2017 American Mathematical Society

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