A geometric classification of some solvable groups of homeomorphisms

C Bleak*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

12 Citations (Scopus)


We investigate subgroups of the group PLo(I) of piecewise-linear, orientation-preserving homeomorphisms of the unit interval with finitely many breaks in slope, under the operation of composition, and also subgroups of generalized Thompson groups F_n. We find geometric criteria determining the derived length of any such group, and use these criteria to produce a geometric classification of the solvable and non-solvable subgroups of PLo(I) and of the F_n. We also show that any standard restricted wreath product (of non-trivial groups) that embeds in PLo(I) or F_n must have T≅ℤ.
Original languageEnglish
Pages (from-to)352-372
Number of pages21
JournalJournal of the London Mathematical Society
Issue number2
Early online date17 Jun 2008
Publication statusPublished - 1 Oct 2008


  • Derived length
  • Solvable groups
  • PL homeomorphisms
  • Thompson's groups
  • Wreath products


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