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

2006/11/07 by Bezuglyi, Sergey, Medynets, Konstantin
#20B99 (Secondary) #37B05 (Primary) #Dynamical Systems (math.DS) #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.math/0611173

Abstract

In the paper, we consider the full group [ϕ] and topological full group [[ϕ]] 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 \citegps: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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