Structure theorems for subgroups of homeomorphisms groups
Group Theory
2011-05-19 v4 Dynamical Systems
Abstract
In this partly expository paper, we study the set A of groups of orientation-preserving homeomorphisms of the circle S^1 which do not admit non-abelian free subgroups. We use classical results about homeomorphisms of the circle and elementary dynamical methods to derive various new and old results about the groups in A. Of the known results, we include some results from a family of results of Beklaryan and Malyutin, and we also give a new proof of a theorem of Margulis. Our primary new results include a detailed classification of the solvable subgroups of R. Thompson's group T .
Cite
@article{arxiv.0910.0218,
title = {Structure theorems for subgroups of homeomorphisms groups},
author = {Collin Bleak and Martin Kassabov and Francesco Matucci},
journal= {arXiv preprint arXiv:0910.0218},
year = {2011}
}
Comments
31 pages, 3 figures; final version, to appear in "International Journal of Algebra and Computation"