On the group of spheromorphisms of a homogeneous non-locally finite tree

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 isomor...

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Veröffentlicht in:	Izvestiya. Mathematics 2020-12, Vol.84 (6), p.1161-1191
1. Verfasser:	Neretin, Yu. A.
Format:	Artikel
Sprache:	eng
Schlagworte:	Apexes Automorphisms Baire space Bruhat-Tits tree continued fraction Irrationality Isomorphism representation of categories Subgroups Thompson group
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description	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 .
doi_str_mv	10.1070/IM8970
format	Article
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subjects	Apexes Automorphisms Baire space Bruhat-Tits tree continued fraction Irrationality Isomorphism representation of categories Subgroups Thompson group
title	On the group of spheromorphisms of a homogeneous non-locally finite tree
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