Translator Disclaimer
December 2011 Finitely approximable groups and actions Part II: Generic representations
Christian Rosendal
J. Symbolic Logic 76(4): 1307-1321 (December 2011). DOI: 10.2178/jsl/1318338851

Abstract

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 of mutually conjugate isometric actions of Γ on ℚ𝕌.

Citation

Download Citation

Christian Rosendal. "Finitely approximable groups and actions Part II: Generic representations." J. Symbolic Logic 76 (4) 1307 - 1321, December 2011. https://doi.org/10.2178/jsl/1318338851

Information

Published: December 2011
First available in Project Euclid: 11 October 2011

zbMATH: 1250.03086
MathSciNet: MR2895397
Digital Object Identifier: 10.2178/jsl/1318338851

Subjects:
Primary: 03E15

Rights: Copyright © 2011 Association for Symbolic Logic

JOURNAL ARTICLE
15 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

SHARE
Vol.76 • No. 4 • December 2011
Back to Top