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An algebraic classification of some solvable groups of homeomorphisms

Collin Bleak
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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.

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Collin Bleak. 2006-04-13. An algebraic classification of some solvable groups of homeomorphisms. https://arxiv.org/abs/math/0602038

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