Short proofs of theorems of Malyutin and Margulis

2016/05/15 by Eli Glasner, Glasner, Eli
Mathematics · #20B07 #37B05 #54H20 #Dynamical Systems (math.DS) #FOS: Mathematics #Group Theory (math.GR) #math.DS #math.GR #msc:20B07 #msc:37B05 #msc:54H20

paper · pdf · doi:10.48550/arxiv.1605.04507

arxiv created 2016/06/03 · arxiv updated 2016/06/06

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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