A geometric classification of some solvable groups of homeomorphisms
arXiv:math/0602036 · doi:10.1112/jlms/jdn017
Abstract
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 the generalized Thompson groups F_n. We find geometric criteria determining the derived length of any such group, and use this 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 C wr T (of non-trivial groups) that embeds in PLo(I) or F_n must have T isomorphic with the integers.
19 pages, in preparation. Portions of this paper contain portions of the author's dissertation written at Binghamton University. Newer versions contain improved grammar, corrected typos and minor re-arrangements