Geodesic
Full groups, flip conjugacy, and orbit equivalence of Cantor minimal systems
S. Bezuglyi1 ; K. Medynets2
1 Institute for Low Temperature Physics National Academy of Sciences of Ukraine Kharkov, Ukraine
2 Insitute for Low Temperature Physics National Academy of Sciences of Ukraine Kharkov, Ukraine
Colloquium Mathematicum, Tome 110 (2008) no. 2, pp. 409-429.

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

We consider the full group $[\varphi ]$ and topological full group $[[\varphi ]]$ of a Cantor minimal system $(X,\varphi )$. We prove that the commutator subgroups $D([\varphi ])$ and $D([[\varphi ]])$ are simple and show that the groups $D([\varphi ])$ and $D([[\varphi ]])$ completely determine the class of orbit equivalence and flip conjugacy of $\varphi $, respectively. These results improve the classification found in [GPS]. As a corollary of the technique used, we establish the fact that $\varphi $ can be written as a product of three involutions from $[\varphi ]$.
DOI : 10.4064/cm110-2-6
Keywords: consider full group varphi topological full group varphi cantor minimal system varphi prove commutator subgroups varphi varphi simple groups varphi varphi completely determine class orbit equivalence flip conjugacy varphi respectively these results improve classification found gps corollary technique establish varphi written product three involutions varphi

S. Bezuglyi 1 ; K. Medynets 2

1 Institute for Low Temperature Physics National Academy of Sciences of Ukraine Kharkov, Ukraine
2 Insitute for Low Temperature Physics National Academy of Sciences of Ukraine Kharkov, Ukraine 
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S. Bezuglyi; K. Medynets. Full groups, flip conjugacy, and orbit equivalence
 of Cantor minimal systems. Colloquium Mathematicum, Tome 110 (2008) no. 2, pp. 409-429. doi : 10.4064/cm110-2-6. http://geodesic.mathdoc.fr/articles/10.4064/cm110-2-6/

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