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

S. Bezuglyi, and K. Medynets. "Full groups, flip conjugacy, and orbit equivalence of Cantor minimal systems." Colloquium Mathematicae 110.2 (2008): 409-429. <http://eudml.org/doc/283755>.

@article{S2008,
abstract = {We consider the full group [φ] and topological full group [[φ]] of a Cantor minimal system (X,φ). We prove that the commutator subgroups D([φ]) and D([[φ]]) are simple and show that the groups D([φ]) and D([[φ]]) completely determine the class of orbit equivalence and flip conjugacy of φ, respectively. These results improve the classification found in [GPS]. As a corollary of the technique used, we establish the fact that φ can be written as a product of three involutions from [φ].},
author = {S. Bezuglyi, K. Medynets},
journal = {Colloquium Mathematicae},
keywords = {Cantor set; minimal homeomorphism; full groups; commutator; involution},
language = {eng},
number = {2},
pages = {409-429},
title = {Full groups, flip conjugacy, and orbit equivalence of Cantor minimal systems},
url = {http://eudml.org/doc/283755},
volume = {110},
year = {2008},
}

TY - JOUR
AU - S. Bezuglyi
AU - K. Medynets
TI - Full groups, flip conjugacy, and orbit equivalence of Cantor minimal systems
JO - Colloquium Mathematicae
PY - 2008
VL - 110
IS - 2
SP - 409
EP - 429
AB - We consider the full group [φ] and topological full group [[φ]] of a Cantor minimal system (X,φ). We prove that the commutator subgroups D([φ]) and D([[φ]]) are simple and show that the groups D([φ]) and D([[φ]]) completely determine the class of orbit equivalence and flip conjugacy of φ, respectively. These results improve the classification found in [GPS]. As a corollary of the technique used, we establish the fact that φ can be written as a product of three involutions from [φ].
LA - eng
KW - Cantor set; minimal homeomorphism; full groups; commutator; involution
UR - http://eudml.org/doc/283755
ER -