Structure theorems for groups of homeomorphisms of the circle

Collin Patrick Bleak, Martin Kassabov, Francesco Matucci

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)


In this partly expository paper, we study the set A 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 A. 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 .
Original languageEnglish
Pages (from-to)1007-1036
Number of pages30
JournalInternational Journal of Algebra and Computation
Issue number6
Publication statusPublished - Sept 2011


  • Rotation number
  • circle maps
  • classification of subgroups
  • solvable subgroups
  • Thompson groups


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