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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)].

##### MSC:
 20E08 Groups acting on trees 20F05 Generators, relations, and presentations of groups
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##### References:
 [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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