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 TH(B(T)) = ⟨Iso(T),V⟩ generated by the group 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).
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm103-2-12,
author = {B. Majcher-Iwanow},
title = {Equivalence relations induced by some locally compact groups of homeomorphisms of $2^{$\mathbb{N}$}$
},
journal = {Colloquium Mathematicae},
volume = {103},
year = {2005},
pages = {287-301},
zbl = {1094.03034},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm103-2-12}
}
B. Majcher-Iwanow. Equivalence relations induced by some locally compact groups of homeomorphisms of $2^{ℕ}$
. Colloquium Mathematicae, Tome 103 (2005) pp. 287-301. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm103-2-12/