Journal of Symbolic Logic
- J. Symbolic Logic
- Volume 76, Issue 3 (2011), 1005-1022.
Completely metrisable groups acting on trees
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.
J. Symbolic Logic, Volume 76, Issue 3 (2011), 1005-1022.
First available in Project Euclid: 6 July 2011
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 20E08: Groups acting on trees [See also 20F65]
Secondary: 03E15: Descriptive set theory [See also 28A05, 54H05]
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