On the height of subgroups of Homeo(I)

Abstract

In [Bl1], it is proved that a subgroup of $P{L}_{+}(I)$ has a finite height if and only if it is solvable. We prove the "only if" part for any subgroup of Homeo${}_{+}(I)$, and present a construction which indicates a plethora of examples of solvable groups with infinite height.

More details added in the proof of Theorem 1.7. Several other minor editing made (improving the grammar and the presentation). arXiv admin note: text overlap with arXiv:math/0602036 by other authors

References in corpus (3)

• Global rigidity of solvable group actions on S^1
• A geometric classification of some solvable groups of homeomorphisms
• Solvability in Groups of Piecewise-linear Homeomorphisms of the Unit Interval