Full groups of minimal homeomorphisms and Baire category methods

Tomás Ibarlucia (1) , Julien Melleray (1)

1 ICJ - Institut Camille Jordan

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 $\Homeo(X)$.

Domaines: Logique [math.LO]; Systèmes dynamiques [math.DS]

Tomás Ibarlucia, Julien Melleray. Full groups of minimal homeomorphisms and Baire category methods. 2014. ⟨hal-00861053v2⟩