Geodesic
Full groups, flip conjugacy, and orbit equivalence of Cantor minimal systems
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
Colloquium Mathematicum, Tome 110 (2008) no. 2, pp. 409-429 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

Voir la notice de l'article

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 
@article{10_4064_cm110_2_6,
     author = {S. Bezuglyi and K. Medynets},
     title = {Full groups, flip conjugacy, and orbit equivalence
 of {Cantor} minimal systems},
     journal = {Colloquium Mathematicum},
     pages = {409--429},
     year = {2008},
     volume = {110},
     number = {2},
     doi = {10.4064/cm110-2-6},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4064/cm110-2-6/}
}
TY  - JOUR
AU  - S. Bezuglyi
AU  - K. Medynets
TI  - Full groups, flip conjugacy, and orbit equivalence
 of Cantor minimal systems
JO  - Colloquium Mathematicum
PY  - 2008
SP  - 409
EP  - 429
VL  - 110
IS  - 2
UR  - http://geodesic.mathdoc.fr/articles/10.4064/cm110-2-6/
DO  - 10.4064/cm110-2-6
LA  - en
ID  - 10_4064_cm110_2_6
ER  - 
%0 Journal Article
%A S. Bezuglyi
%A K. Medynets
%T Full groups, flip conjugacy, and orbit equivalence
 of Cantor minimal systems
%J Colloquium Mathematicum
%D 2008
%P 409-429
%V 110
%N 2
%U http://geodesic.mathdoc.fr/articles/10.4064/cm110-2-6/
%R 10.4064/cm110-2-6
%G en
%F 10_4064_cm110_2_6
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

Cité par Sources :