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September 2011 Completely metrisable groups acting on trees
Christian Rosendal
J. Symbolic Logic 76(3): 1005-1022 (September 2011). DOI: 10.2178/jsl/1309952531

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.

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Christian Rosendal. "Completely metrisable groups acting on trees." J. Symbolic Logic 76 (3) 1005 - 1022, September 2011. https://doi.org/10.2178/jsl/1309952531

Information

Published: September 2011
First available in Project Euclid: 6 July 2011

zbMATH: 1268.20028
MathSciNet: MR2849256
Digital Object Identifier: 10.2178/jsl/1309952531

Subjects:
Primary: 20E08
Secondary: 03E15

Rights: Copyright © 2011 Association for Symbolic Logic

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Vol.76 • No. 3 • September 2011
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