Retracts of vertex sets of trees and the almost stability theorem

Abstract

Let G be a group, let T be an (oriented) G-tree with finite edge stabilizers, and let VT denote the vertex set of T. We show that, for each G-retract V' of the G-set VT, there exists a G-tree whose edge stabilizers are finite and whose vertex set is V'. This fact leads to various new consequences of the almost stability theorem. We also give an example of a group G, a G-tree T and a G-retract V' of VT such that no G-tree has vertex set V'.

15 pages, 0 figures. Formerly titled "Some refinements of the almost stability theorem". Version 3

References in corpus (1)

• Deformation and rigidity of simplicial group actions on trees

Cited by in corpus (1)

• Non-orientable surface-plus-one-relation groups