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Finitely approximable groups and actions Part II: Generic representations

Published online by Cambridge University Press:  12 March 2014

Christian Rosendal
Christian Rosendal*
Affiliation:
Department of Mathematics, Statistics, and Computer Science (M/C 249), University of Illinoisat Chicago, 851 S. Morgan St., Chicago, IL 60607-7045, USA, E-mail: rosendal.math@gmail.com, URL: http://www.math.uic.edu/~rosendal
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Abstract

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

Keywords

Urysohn metric spacesubgroup separable groupsisometry groups
Type
Research Article
Information
The Journal of Symbolic Logic , Volume 76 , Issue 4 , December 2011 , pp. 1307 - 1321
Copyright
Copyright © Association for Symbolic Logic 2011

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