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Journal of the London Mathematical Society Advance Access published online on June 17, 2008
Journal of the London Mathematical Society, doi:10.1112/jlms/jdn017
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© 2008 London Mathematical Society

A geometric classification of some solvable groups of homeomorphisms

Collin Bleak

Department of Mathematics
University of Nebraska–Lincoln
203 Avery Hall
Lincoln, NE 68588
USA

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 Fn. 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 Fn. We also show that any standard restricted wreath product Formula (of non-trivial groups) that embeds in PLo(I) or Fn must have T{cong} Z.

2000 Mathematics Subject Classification 20E45, 20F37, 20F60.

Received April 13, 2006; revised January 28, 2008;
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