Retracts of vertex sets of trees and the almost stability theorem

Details Retracts of vertex sets of trees and the almost stability theorem Retracts of vertex sets of trees and the almost stability theorem

2005-10-07

arxiv.org/abs/math/0510151v3

J. Group Theory 10 (2007), 703-721.

Mathematics

Group Theory

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

Scientific paper

10.1515/JGT.2007.051

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'.

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