Full groups, flip conjugacy, and orbit equivalence
of Cantor minimal systems
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 $[\varphi ]$.
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
Affiliations des auteurs :
S. Bezuglyi 1 ; K. Medynets 2
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author = {S. Bezuglyi and K. Medynets},
title = {Full groups, flip conjugacy, and orbit equivalence
of {Cantor} minimal systems},
journal = {Colloquium Mathematicum},
pages = {409--429},
publisher = {mathdoc},
volume = {110},
number = {2},
year = {2008},
doi = {10.4064/cm110-2-6},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/cm110-2-6/}
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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
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