On uniqueness of JSJ decompositions of finitely generated groups
Group Theory
2007-05-23 v2 Geometric Topology
Abstract
We give an example of two JSJ decompositions of a group that are not related by conjugation, conjugation of edge-inclusions, and slide moves. This answers the question of Rips and Sela stated in "Cyclic splittings of finitely presented groups and the canonical JSJ decomposition," Ann. of Math. 146 (1997), 53-109. On the other hand we observe that any two JSJ decompositions of a group are related by an elementary deformation, and that strongly slide-free JSJ decompositions are genuinely unique. These results hold for the decompositions of Rips and Sela, Dunwoody and Sageev, and Fujiwara and Papasoglu, and also for accessible decompositions.
Keywords
Cite
@article{arxiv.math/0110176,
title = {On uniqueness of JSJ decompositions of finitely generated groups},
author = {Max Forester},
journal= {arXiv preprint arXiv:math/0110176},
year = {2007}
}
Comments
11 pages; shortened and reorganized; mathematical content unchanged