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Finitely Approximate Groups and Actions Part II: Generic Representations

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journal contribution
posted on 14.08.2012, 00:00 by Christian Rosendal
Given a finitely generated group Γ, we study the space Isom(Γ,QU) of all actions of Γ by isometries of the rational Urysohn metric space QU, where Isom(Γ, QU) is equipped with the topology it inherits seen as a closed subset of Isom(QU)Γ. When Γ is the free group Fn on n generators this space is just Isom(QU)n, but is in general significantly more complicated. We prove that when Γ is finitely generated Abelian there is a generic point in Isom(Γ, QU), i.e., there is a comeagre set ofmutually conjugate isometric actions of Γ on QU.

Funding

The author was partially supported by NSF grants DMS 0901405 and DMS 0919700. The author is also grateful for the many helpful suggestions of the referee.

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Publisher Statement

© 2011, Association for Symbolic Logic. The original version is available through Association for Symbolic Logic at DOI: 644mpo9untexw1`10.2178/jsl/1318338851

Publisher

Association for Symbolic Logic

Language

en_US

issn

0022-4812

Issue date

01/12/2011

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