Group actions on \({\mathbb{R}}\)-trees. (English) Zbl 0658.20021

Culler, Marc; Morgan, John W.

Proc. Lond. Math. Soc., III. Ser. 55, 571-604 (1987).

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

Keywords:

group-actions on \({\mathbb{R}}\)-trees; isometries of \({\mathbb{R}}\)-trees; isometries of hyperbolic space; groups of isometries; finitely generated group