An algebraic classification of some solvable groups of homeomorphisms

Details An algebraic classification of some solvable groups of homeomorphisms An algebraic classification of some solvable groups of homeomorphisms

2006-02-02

arxiv.org/abs/math/0602038v2

Mathematics

Group Theory

29 pages, 1 figure, preprint. This version has an improved introduction (better references, for instance), and a completely re

Scientific paper

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.

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