- Title
- Willis theory via graphs
- Creator
- Bywaters, Timothy; Tornier, Stephen
- Relation
- Groups, Geometry, and Dynamics Vol. 13, Issue 4, p. 1335-1372
- Publisher Link
- http://dx.doi.org/10.4171/ggd/525
- Publisher
- E M S Press
- Resource Type
- journal article
- Date
- 2019
- Description
- We study the scale and tidy subgroups of an endomorphism of a totally disconnected locally compact group using a geometric framework. This leads to new interpretations of tidy subgroups and the scale function. Foremost, we obtain a geometric tidying procedure which applies to endomorphisms as well as a geometric proof of the fact that tidiness is equivalent to being minimizing for a given endomorphism. Our framework also yields an endomorphism version of the Baumgartner–Willis tree representation theorem. We conclude with a construction of new endomorphisms of totally disconnected locally compact groups from old via HNN-extensions.
- Subject
- totally disconnected locally compact group; scale function; tidy subgroups; endomorphisms of group; permutation groups; groups act on graphs
- Identifier
- http://hdl.handle.net/1959.13/1444317
- Identifier
- uon:42266
- Identifier
- ISSN:1661-7207
- Language
- eng
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