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Completely metrisable groups acting on trees

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 Illinois at Chicago, 851 S. Morgan St., Chicago, Il 60607-7045, USA, E-mail: [email protected], URL: http://www.math.uic.edu/~rosendal
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Abstract

We consider actions of completely metrisable groups on simplicial trees in the context of the Bass–Serre theory. Our main result characterises continuity of the amplitude function corresponding to a given action. Under fairly mild conditions on a completely metrisable group G, namely, that the set of elements generating a non-discrete or finite subgroup is somewhere dense, we show that in any decomposition as a free product with amalgamation, G = A *cB, the amalgamated groups A, B and C are open in G.

Keywords

Primary: 20E08Secondary: 03E15completely metrisable groupslocally compact groupsactions on treesBass–Serre theory
Type
Research Article
Information
The Journal of Symbolic Logic , Volume 76 , Issue 3 , September 2011 , pp. 1005 - 1022
Copyright
Copyright © Association for Symbolic Logic 2011

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