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On Følner sets in topological groups

Part of: Abstract harmonic analysis Connections with other structures, applications Topological and differentiable algebraic systems

Published online by Cambridge University Press:  16 May 2018

Friedrich Martin Schneider  and
Andreas Thom
Friedrich Martin Schneider
Affiliation:
Institute of Algebra, TU Dresden, 01062 Dresden, Germany email martin.schneider@tu-dresden.de
Andreas Thom
Affiliation:
Institute of Geometry, TU Dresden, 01062 Dresden, Germany email andreas.thom@tu-dresden.de
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Abstract

We extend Følner’s amenability criterion to the realm of general topological groups. Building on this, we show that a topological group $G$ is amenable if and only if its left-translation action can be approximated in a uniform manner by amenable actions on the set  $G$ . As applications we obtain a topological version of Whyte’s geometric solution to the von Neumann problem and give an affirmative answer to a question posed by Rosendal.

Keywords

topological groupamenabilityalmost invarianceparadoxicalitycoarse geometry

MSC classification

Primary: 54H11: Topological groups 54H20: Topological dynamics 22A10: Analysis on general topological groups 43A07: Means on groups, semigroups, etc.; amenable groups
Type
Research Article
Information
Compositio Mathematica , Volume 154 , Issue 7 , July 2018 , pp. 1333 - 1361
Copyright
© The Authors 2018 

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