Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Fundamental group of uniquely ergodic Cantor minimal systems   We introduce the fundamental group ${\mathcal F}(\mathcal{R}_{G, \phi})$ of a
uniquely ergodic Cantor minimal $G$-system $\mathcal{R}_{G, \phi}$ where $G$ is
a countable discrete group. We compute fundamental groups of several uniquely
ergodic Cantor minimal $G$-systems. We show that if $\mathcal{R}_{G, \phi}$
arises from a free action $\phi$ of a finitely generated abelian group, then
there exists a unital countable subring $R$ of $\mathbb{R}$ such that
$\mathcal{F}(\mathcal{R}_{G, \phi})=R_{+}^\times$. We also consider the
relation between fundamental groups of uniquely ergodic Cantor minimal
$\mathbb{Z}^n$-systems and fundamental groups of crossed product $C^*$-algebras
$C(X)\rtimes_{\phi} \mathbb{Z}^n$.

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The categories of this paper are: gr-qc
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The categories of this paper are: nlin
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The categories of this paper are: bayes-an
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The categories of this paper are: eess
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The categories of this paper are: dg-ga
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The categories of this paper are: math-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: solv-int
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The categories of this paper are: funct-an
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The categories of this paper are: chao-dyn
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The categories of this paper are: econ
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The categories of this paper are: hep-ex
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The categories of this paper are: cs
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The categories of this paper are: cmp-lg
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The categories of this paper are: adap-org
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The categories of this paper are: acc-phys