Abstract
Abstract
We consider a tree
all whose vertices have countable valency. Its boundary is the Baire space
and the set of irrational numbers
is identified with
by continued fraction expansions. Removing
edges from
, we get a forest consisting of copies of
. A spheromorphism (or hierarchomorphism) of
is an isomorphism of two such subforests regarded as a transformation of
or
. We denote the group of all spheromorphisms by
. We show that the correspondence
sends the Thompson group realized by piecewise
-transformations to a subgroup of
. We construct some unitary representations of
, show that the group
of automorphisms is spherical in
and describe the train (enveloping category) of
.