Willis theory via graphs

  • Timothy P. Bywaters

    The University of Sydney, Australia
  • Stephan Tornier

    The University of Newcastle, Callaghan, Australia
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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.

Cite this article

Timothy P. Bywaters, Stephan Tornier, Willis theory via graphs. Groups Geom. Dyn. 13 (2019), no. 4, pp. 1335–1372

DOI 10.4171/GGD/525