TY - JOUR
T1 - Topological full groups and t.d.l.c. completions of Thompson’s V
AU - Lederle, Waltraud
N1 - Funding Information:
This work was partially supported by Israel Science Foundation grant ISF 2095/15.
Publisher Copyright:
© 2020, Springer-Verlag GmbH Germany, part of Springer Nature.
PY - 2020/12/1
Y1 - 2020/12/1
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=85089297665&partnerID=8YFLogxK
U2 - 10.1007/s00208-020-02063-9
DO - 10.1007/s00208-020-02063-9
M3 - Article
AN - SCOPUS:85089297665
SN - 0025-5831
VL - 378
SP - 1415
EP - 1434
JO - Mathematische Annalen
JF - Mathematische Annalen
IS - 3-4
ER -