Willis Theory via Graphs

Timothy P. Bywaters; Stephan Tornier

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arXiv · 1711.09610

Willis Theory via Graphs

Timothy P. Bywaters·Stephan Tornier

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Abstract

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.

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Timothy P. Bywaters, Stephan Tornier. 2017-11-27. Willis Theory via Graphs. https://arxiv.org/abs/1711.09610

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