Geodesic
A map maintaining the orbits of a given $\mathbb {Z}^d$-action
Bartosz Frej 1   ; Agata Kwaśnicka 1
1 Faculty of Pure and Applied Mathematics Wrocław University of Technology Wybrzeże Wyspiańskiego 27 50-370 Wrocław, Poland
Colloquium Mathematicum, Tome 143 (2016) no. 1, pp. 1-15 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
DOI : 10.4064/cm6361-12-2015
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

Bartosz Frej  1   ; Agata Kwaśnicka  1

1 Faculty of Pure and Applied Mathematics Wrocław University of Technology Wybrzeże Wyspiańskiego 27 50-370 Wrocław, Poland 
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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

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