A map maintaining the orbits of a given $\mathbb {Z}^d$-action
Colloquium Mathematicum, Tome 143 (2016) no. 1, pp. 1-15
Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences
Giordano et al. (2010) showed that every minimal free $\mathbb {Z}^d$-action of a Cantor space $X$ is orbit equivalent to some $\mathbb {Z}$-action. Trying to avoid the K-theory used there and modifying Forrest's (2000) construction of a Bratteli diagram, we show how to define a (one-dimensional) continuous and injective map $F$ on $X\setminus \{\textrm {one point}\}$ such that for a residual subset of $X$ the orbits of $F$ are the same as the orbits of a given minimal free $\mathbb {Z}^d$-action.
Keywords:
giordano showed every minimal mathbb d action cantor space orbit equivalent mathbb action trying avoid k theory there modifying forrests construction bratteli diagram define one dimensional continuous injective map setminus textrm point residual subset orbits the orbits given minimal mathbb d action
Affiliations des auteurs :
Bartosz Frej 1 ; Agata Kwaśnicka 1
@article{10_4064_cm6361_12_2015,
author = {Bartosz Frej and Agata Kwa\'snicka},
title = {A map maintaining the orbits of a given $\mathbb {Z}^d$-action},
journal = {Colloquium Mathematicum},
pages = {1--15},
publisher = {mathdoc},
volume = {143},
number = {1},
year = {2016},
doi = {10.4064/cm6361-12-2015},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/cm6361-12-2015/}
}
TY - JOUR
AU - Bartosz Frej
AU - Agata Kwaśnicka
TI - A map maintaining the orbits of a given $\mathbb {Z}^d$-action
JO - Colloquium Mathematicum
PY - 2016
SP - 1
EP - 15
VL - 143
IS - 1
PB - mathdoc
UR - http://geodesic.mathdoc.fr/articles/10.4064/cm6361-12-2015/
DO - 10.4064/cm6361-12-2015
LA - en
ID - 10_4064_cm6361_12_2015
ER -
%0 Journal Article
%A Bartosz Frej
%A Agata Kwaśnicka
%T A map maintaining the orbits of a given $\mathbb {Z}^d$-action
%J Colloquium Mathematicum
%D 2016
%P 1-15
%V 143
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.4064/cm6361-12-2015/
%R 10.4064/cm6361-12-2015
%G en
%F 10_4064_cm6361_12_2015
Bartosz Frej; Agata Kwaśnicka. A map maintaining the orbits of a given $\mathbb {Z}^d$-action. Colloquium Mathematicum, Tome 143 (2016) no. 1, pp. 1-15. doi: 10.4064/cm6361-12-2015
Cité par Sources :