Topological full groups and t.d.l.c. completions of Thompson’s V

Waltraud Lederle

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

We show that every topological full group coming from a one-sided irreducible shift of finite type, in the sense of Matui, is isomorphic to a group of tree almost automorphisms preserving an edge colouring of the tree. As an application, we prove that it admits totally disconnected, locally compact completions of arbitrary nonempty finite local prime content. The completions we construct have open, simple commutator subgroup. Our results apply to Thompson’s V, providing answers to two questions asked by Le Boudec and Wesolek.

Original languageEnglish
Pages (from-to)1415-1434
Number of pages20
JournalMathematische Annalen
Volume378
Issue number3-4
DOIs
StatePublished - 1 Dec 2020
Externally publishedYes

ASJC Scopus subject areas

  • General Mathematics

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