Journal of Symbolic Logic

Completely metrisable groups acting on trees

Christian 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.

Article information

Source
J. Symbolic Logic, Volume 76, Issue 3 (2011), 1005-1022.

Dates
First available in Project Euclid: 6 July 2011

Permanent link to this document
https://projecteuclid.org/euclid.jsl/1309952531

Digital Object Identifier
doi:10.2178/jsl/1309952531

Mathematical Reviews number (MathSciNet)
MR2849256

Zentralblatt MATH identifier
1268.20028

Subjects
Primary: 20E08: Groups acting on trees [See also 20F65]
Secondary: 03E15: Descriptive set theory [See also 28A05, 54H05]

Keywords
completely metrisable groups locally compact groups actions on trees Bass—Serre theory

Citation

Rosendal, Christian. Completely metrisable groups acting on trees. J. Symbolic Logic 76 (2011), no. 3, 1005--1022. doi:10.2178/jsl/1309952531. https://projecteuclid.org/euclid.jsl/1309952531


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