Short proofs of theorems of Malyutin and Margulis
Eli Glasner

TL;DR
This paper provides a concise proof of Malyutin's theorem on minimal circle actions and uses it to confirm Margulis' theorem, supporting the Ghys-Margulis alternative through the application of enveloping semigroup techniques.
Contribution
It introduces a shorter proof of Malyutin's theorem and derives Margulis' theorem, simplifying the understanding of the Ghys-Margulis alternative.
Findings
Short proof of Malyutin's theorem
Confirmation of Margulis' theorem
Support for the Ghys-Margulis alternative
Abstract
The Ghys-Margulis alternative asserts that a subgroup 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 . 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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