Equivalence relations induced by some locally compact groups of homeomorphisms of $2^{\mathbb {N}}$
Volume 103 / 2005
Colloquium Mathematicum 103 (2005), 287-301
MSC: 03E15, 20E08.
DOI: 10.4064/cm103-2-12
Abstract
Let $T$ be a locally finite rooted tree and $B(T)$ be the boundary space of $T$. We study locally compact subgroups of the group ${\rm TH}(B(T))=\langle {\rm Iso}(T),V\rangle$ generated by the group ${\rm Iso}(T)$ of all isometries of $B(T)$ and the group $V$ of Richard Thompson. We describe orbit equivalence relations arising from actions of these groups on $B(T)$.
