Short proofs of theorems of Malyutin and Margulis

Glasner, Eli

doi:10.1090/proc/13664

Short proofs of theorems of Malyutin and Margulis
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Proc. Amer. Math. Soc. 145 (2017), 5463-5467 Request permission

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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