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Group actions on $${\mathbb{R}}$$-trees. (English) Zbl 0658.20021
There are two features of group-actions on $${\mathbb{R}}$$-trees which are addressed in this paper. The first is that isometries of $${\mathbb{R}}$$-trees behave in many ways like isometries of hyperbolic space, and that groups of isometries of $${\mathbb{R}}$$-trees resemble subgroups of SO(n,1). The second is that, for a fixed finitely generated group G, the space of all actions of G on $${\mathbb{R}}$$-trees has strong compactness properties.

##### MSC:
 20F34 Fundamental groups and their automorphisms (group-theoretic aspects) 57N10 Topology of general $$3$$-manifolds (MSC2010) 57S20 Noncompact Lie groups of transformations 57M05 Fundamental group, presentations, free differential calculus 20F28 Automorphism groups of groups
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