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arXiv · 1605.04507

Short proofs of theorems of Malyutin and Margulis

Eli Glasner
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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 the use of the apparatus of the enveloping semigroup enables us to shorten the proof considerably.

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Eli Glasner. 2016-06-03. Short proofs of theorems of Malyutin and Margulis. https://arxiv.org/abs/1605.04507

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