We establish a new connection between local and large-scale structure in compactly generated totally disconnected locally compact (t.d.l.c.) groups G, finding a sufficient condition for G to have more than one end in terms of its compact subgroups. The condition actually results in an action of a quotient group G/N on a tree with faithful micro-supported action on the boundary, where N is compact, and is closely related to the Boolean algebra formed by the centralisers of the subgroups of G/N with open normaliser. As an application, we find a sufficient condition, given a one-ended t.d.l.c. group G, for all direct factors of open subgroups of G to be trivial or open.
Pierre-Emmanuel Caprace
1
;
Timothée Marquis
1
;
Colin D. Reid
2
1
Université Catholique de Louvain, Louvain-la-Neuve, Belgium
2
University of Newcastle, Callaghan, Australia
Pierre-Emmanuel Caprace; Timothée Marquis; Colin D. Reid. Growing trees from compact subgroups. Groups, geometry, and dynamics, Tome 18 (2024) no. 1, pp. 327-352. doi: 10.4171/ggd/759
@article{10_4171_ggd_759,
author = {Pierre-Emmanuel Caprace and Timoth\'ee Marquis and Colin D. Reid},
title = {Growing trees from compact subgroups},
journal = {Groups, geometry, and dynamics},
pages = {327--352},
year = {2024},
volume = {18},
number = {1},
doi = {10.4171/ggd/759},
url = {http://geodesic.mathdoc.fr/articles/10.4171/ggd/759/}
}
TY - JOUR
AU - Pierre-Emmanuel Caprace
AU - Timothée Marquis
AU - Colin D. Reid
TI - Growing trees from compact subgroups
JO - Groups, geometry, and dynamics
PY - 2024
SP - 327
EP - 352
VL - 18
IS - 1
UR - http://geodesic.mathdoc.fr/articles/10.4171/ggd/759/
DO - 10.4171/ggd/759
ID - 10_4171_ggd_759
ER -
%0 Journal Article
%A Pierre-Emmanuel Caprace
%A Timothée Marquis
%A Colin D. Reid
%T Growing trees from compact subgroups
%J Groups, geometry, and dynamics
%D 2024
%P 327-352
%V 18
%N 1
%U http://geodesic.mathdoc.fr/articles/10.4171/ggd/759/
%R 10.4171/ggd/759
%F 10_4171_ggd_759
