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.


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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