Growing trees from compact subgroups
(2024) Groups, Geometry, and Dynamics — Vol. 18, n° 1, p. 327-352 (2024)
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- Authors
Reid, Colin D. 
- Abstract
- 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 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 locally normal subgroups of G/N. 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.
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Citations
Caprace, P.-E., Marquis, T., & Reid, C. D. (2024). Growing trees from compact subgroups. Groups, Geometry, and Dynamics, 18(1), 327-352. https://doi.org/10.4171/ggd/759 (Original work published 2024)