Commentarii Mathematici Helvetici
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Published online: 2003-12-31
On uniqueness of JSJ decompositions of finitely generated groupsMax Forester (1) University of Warwick, Coventry, UK
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 [RS]. 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: G-tree, JSJ decomposition, splitting, Baumslag-Solitar group, accessible group
Forester Max: On uniqueness of JSJ decompositions of finitely generated groups. Comment. Math. Helv. 78 (2003), 740-751. doi: 10.1007/s00014-003-0780-y