Growing trees from compact subgroups

Title: Growing trees from compact subgroups
Creator: Caprace, Pierre-Emmanuel; Marquis, Timothee; Reid, Colin D.
Relation: ARC.FL170100032 http://purl.org/au-research/grants/arc/FL170100032
Relation: Groups, Geometry, and Dynamics Vol. 18, Issue 1, p. 327-352
Publisher Link: http://dx.doi.org/10.4171/GGD/759
Publisher: EMS Press
Resource Type: journal article
Date: 2024
Description: 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.
Subject: locally compact groups; actions on trees; micro-supported actions
Identifier: http://hdl.handle.net/1959.13/1500673
Identifier: uon:54985
Identifier: ISSN:1661-7207
Language: eng
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