On uniqueness of JSJ decompositions of finitely generated groups
By Max Forester. 2001
57 citations recorded by the source corpus.
AbstractWe 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.
Subfields: Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/810f8acd8615e4c4d0535d516957fae6de7229e4
How researchers see this paper
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In Geometry and Topology
- Vincent Guirardel
- Gilbert Levitt
- Max Forester
- Alessandro Sisto
- Henry Wilton
- Franccois Dahmani
- Denis V. Osin
- Michael Hull
In Mathematical Physics
- Gilbert Levitt
- Vincent Guirardel
- Max Forester
- Franccois Dahmani
- Alessandro Sisto
- Henry Wilton
- Denis V. Osin
- Radhika Gupta
Citations in the corpus
- Deformation and rigidity of simplicial group actions on trees (2001, background): “These applications are described in detail in [9].”
- Quotients and subgroups of Baumslag–Solitar groups (2013, background): “1 Generalities on GBS groups We refer to [9, 10, 12] for basic facts about GBS groups.”
- Trees of cylinders and canonical splittings (2008, background): “In general, JSJ splittings are not unique, and there is a whole space of JSJ splittings called the JSJ deformation space; see Forester [10] and the authors’ paper [17].”
- Deformation spaces of trees (2006, background): “Though canonical, they are only unique up to certain moves (see the above references, as well as [17], [4], [31]).”