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Analogues of Cayley graphs for topological groups

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Abstract

We define for a compactly generated totally disconnected locally compact group a graph, called a rough Cayley graph, that is a quasi-isometry invariant of the group. This graph carries information about the group structure in an analogous way to the ordinary Cayley graph for a finitely generated group. With this construction the machinery of geometric group theory can be applied to topological groups. This is illustrated by a study of groups where the rough Cayley graph has more than one end and a study of groups where the rough Cayley graph has polynomial growth.

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Author notes

  1. Bernhard Krön

    Present address: Mathematisches Seminar der Universität Hamburg, Bundesstr. 55, 20146, Hamburg, Germany

Authors and Affiliations

  1. School of Mathematics and Statistics, The University of Sydney, Sydney, NSW, 2006, Australia

    Bernhard Krön

  2. Science Institute, University of Iceland, Dunhaga 3, 107, Reykjavík, Iceland

    Rögnvaldur G. Möller

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  1. Bernhard Krön
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  2. Rögnvaldur G. Möller
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Correspondence to Rögnvaldur G. Möller.

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Supported by project J2245 of the Austrian Science Fund (FWF) and be an IEF Marie Curie Fellowship of the Commission of the European Union.

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Krön, B., Möller, R.G. Analogues of Cayley graphs for topological groups. Math. Z. 258, 637–675 (2008). https://doi.org/10.1007/s00209-007-0190-8

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