Full groups of minimal homeomorphisms

Tomás Ibarlucia; Julien Melleray

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arXiv · 1309.3114

Full groups of minimal homeomorphisms

Tomás Ibarlucia·Julien Melleray

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Abstract

We study full groups of minimal actions of countable groups by homeomorphisms on a Cantor space $X$, showing that these groups do not admit a compatible Polish group topology and, in the case of $\Z$-actions, are coanalytic non-Borel inside $\Homeo(X)$. We point out that the full group of a minimal homeomorphism is topologically simple. We also study some properties of the closure of the full group of a minimal homeomorphism inside $\Homeo(X)$.

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BibTeX RIS

Tomás Ibarlucia, Julien Melleray. 2014-02-03. Full groups of minimal homeomorphisms. https://arxiv.org/abs/1309.3114

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