Retracts of vertex sets of trees and the almost stability theorem
Group Theory
2011-11-09 v3
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'.
Cite
@article{arxiv.math/0510151,
title = {Retracts of vertex sets of trees and the almost stability theorem},
author = {Warren Dicks and M. J. Dunwoody},
journal= {arXiv preprint arXiv:math/0510151},
year = {2011}
}
Comments
15 pages, 0 figures. Formerly titled "Some refinements of the almost stability theorem". Version 3