Groups acting on \(\mathbb{R}\)-trees. (English) Zbl 0767.20011

Given an almost finitely presented group \(G\) with free action on a minimal \(\mathbb{R}\)-tree \(T\), the author constructs a similar \(\mathbb{R}\)-tree \(T'\) and a \(G\)-morphism \(\phi:T' \rightarrow T\) for which \(T'\) has certain nice properties, e.g. there is a bound on the number of vertex orbits.
For the case of simplicial \(\mathbb{R}\)-trees, see Ch. 6 of W. Dicks and M. J. Dunwoody [Groups acting on graphs (1989; Zbl 0665.20001)].


20E08 Groups acting on trees
20F05 Generators, relations, and presentations of groups


Zbl 0665.20001
Full Text: DOI


[1] Dicks, W. 1989. ”Groups acting on graphs”. Cambridge: Cambridge University Press. · Zbl 0665.20001
[2] DOI: 10.1016/0040-9383(87)90005-X · Zbl 0623.57013
[3] Shalen, P.B. 1987. ”Dendrology of groups: an introduction, in Essays in group theory”. Edited by: Gersten, S.M. Vol. 8, 265–320. MSRI Publications. Springer
[4] DOI: 10.1090/S0273-0979-1990-15907-5 · Zbl 0708.30044
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