An algebraic classification of some solvable groups of homeomorphisms

2006/02/02 by Bleak, Collin
#20F38 #FOS: Mathematics #General Topology (math.GN) #Group Theory (math.GR)

paper · doi:10.48550/arxiv.math/0602038

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.

Related

• Solvability in Groups of Piecewise-linear Homeomorphisms of the Unit Interval
• Determining solubility for finitely generated groups of PL\n homeomorphisms
• A Minimal Non-solvable Group of Homeomorphisms
• Algorithms and Classification in Groups of Piecewise-Linear Homeomorphisms
• On Groups of PL-homeomorphisms of the Real Line