JSJ-Decompositions of finitely presented groups and complexes of groups

By K. Fujiwara, Panos Papasoglu. 2005

82 citations recorded by the source corpus.

Abstract.A JSJ-splitting of a group G over a certain class of subgroups is a graph of groups decomposition of G which describes all possible decompositions of G as an amalgamated product or an HNN extension over subgroups lying in the given class. Such decompositions originated in 3-manifold topology. In this paper we generalize the JSJ-splitting constructions of Sela, Rips–Sela and Dunwoody–Sageev, and we construct a JSJ-splitting for any finitely presented group with respect to the class of all slender subgroups along which the group splits. Our approach relies on Haefliger’s theory of group actions on CAT(0) spaces.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/51c16150f6d29a12e7a6b6987fb94794b93c4072

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In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Effective JSJ Decompositions (2004, methodology): “More general approaches to JSJ decompositions of groups have been described by Dunwoody and Sageev [19] and by Fujiwara and Papasoglu [22].”
The Isomorphism Problem for All Hyperbolic Groups (2010, methodology): “It coincides with Bowditch’s decomposition [Bow] and has been widely studied ([DuS], [ FP ]), but we still do not know whether it is computable.”
Three-Dimensional Orbifolds and Their Geometric Structures (2003, background): “The reader is referred to the original papers [29, 61, 62, 75, 98].”
Deformation spaces of trees (2006, methodology): “JSJ decompositions of finitely presented groups have been constructed by Rips–Sela [30], Dunwoody– Sageev [15], Fujiwara–Papasoglu [19].”
Trees of cylinders and canonical splittings (2008, background): “In group theory, a JSJ splitting of a group G is a splitting of G (as a graph of groups) in which one can read any splitting of G and which is maximal for this property; see Sela [28], Rips and Sela [25], Dunwoody and Sageev [8], Fujiwara and Papasoglu [11], Bowditch [1], and the authors’ papers [12”
On uniqueness of JSJ decompositions of finitely generated groups (2001, methodology): “A similar argument shows that any generalized Baumslag–Solitar tree as above is also a JSJ decomposition over 2–ended groups in the sense of Dunwoody and Sageev [DS], and a JSJ decomposition over slender groups in the sense of Fujiwara and Papasoglu [FP].”