Full groups, flip conjugacy, and orbit equivalence of Cantor minimal systems

Details Full groups, flip conjugacy, and orbit equivalence of Cantor minimal systems Full groups, flip conjugacy, and orbit equivalence of Cantor minimal systems

2006-11-07

arxiv.org/abs/math/0611173v3

Mathematics

Dynamical Systems

17 pages, references added, some typos fixed

Scientific paper

In the paper, we consider the full group $[\phi]$ and topological full group $[[\phi]]$ of a Cantor minimal system $(X,\f)$. We prove that the commutator subgroups $D([\f])$ and $D([[\f]])$ are simple and show that the groups $D([\f])$ and $D([[\f]])$ completely determine the class of orbit equivalence and flip conjugacy of $\f$, respectively. These results improve the classification found in \cite{gps:1999}. As a corollary of the technique used, we establish the fact that $\f$ can be written as a product of three involutions from $[\f]$.

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