Margulis, Gregory Free subgroups of the homeomorphism group of the circle. (English. Abridged French version) Zbl 0983.37029 C. R. Acad. Sci., Paris, Sér. I, Math. 331, No. 9, 669-674 (2000). From the author’s abstract: “Tits’ alternative says that a finitely generated linear group either contains a noncommutative free subgroup or is virtually solvable. It is known that an analogue of Tits’ alternative is not true for subgroups of the group Homeo\((S^1)\) of all homeomorphisms of the circle \(S^1\) and even for subgroups of the group of \(C^\infty\)-diffeomorphisms of \(S^1\). The main purpose of this Note is to prove a conjecture of E. Ghys which can be viewed as a replacement of Tits’ alternative for Homeo\((S^1)\) and which says that if \(G\) is a subgroup of Homeo\((S^1)\) containing no free noncommutative subgroup then there is a \(G\)-invariant probability measure on \(S^1\).”The paper under review is well written and organized and has high level. Reviewer: Alois Klíč (Praha) Cited in 2 ReviewsCited in 31 Documents MSC: 37C85 Dynamics induced by group actions other than \(\mathbb{Z}\) and \(\mathbb{R}\), and \(\mathbb{C}\) 57S05 Topological properties of groups of homeomorphisms or diffeomorphisms 57S25 Groups acting on specific manifolds 37E10 Dynamical systems involving maps of the circle Keywords:minimal action; finitely generated group; quasi-Schottky group; invariant measure × Cite Format Result Cite Review PDF Full Text: DOI