An algebraic classification of some solvable groups of homeomorphisms
Abstract
We produce two separate algebraic descriptions of the isomorphism classes of the solvable subgroups of the group PLo(I) of piecewise-linear orientation-preserving homeomorphisms of the unit interval under the operation of composition, and also of the solvable subgroups of the generalized R. Thompson groups F_n. The first description is as a set of isomorphism classes of groups which is closed under three algebraic operations, and the second is as the set of isomorphism classes of subgroups of a countable collection of easily described groups. We show the two descriptions are equivalent.
Keywords
Cite
@article{arxiv.math/0602038,
title = {An algebraic classification of some solvable groups of homeomorphisms},
author = {Collin Bleak},
journal= {arXiv preprint arXiv:math/0602038},
year = {2007}
}
Comments
29 pages, 1 figure, preprint. This version has an improved introduction (better references, for instance), and a completely re-written section on the split group. The section on the split group is more detailed and corrects a minor inaccuracy