STRUCTURE THEOREMS FOR GROUPS OF HOMEOMORPHISMS OF THE CIRCLE

Abstract

In this partly expository paper, we study the set [Formula: see text] of groups of orientation-preserving homeomorphisms of the circle S 1 which do not admit non-abelian free subgroups. We use classical results about homeomorphisms of the circle and elementary dynamical methods to derive various new and old results about the groups in [Formula: see text]. Of the known results, we include some results from a family of results of Beklaryan and Malyutin, and we also give a new proof of a theorem of Margulis. Our primary new results include a detailed classification of the solvable subgroups of R. Thompson's group T.