JSJ decompositions: definitions, existence, uniqueness. I: The JSJ deformation space

Abstract

This paper and its companion arXiv:1002.4564 have been replaced by arXiv:1602.05139. We give a general simple definition of JSJ decompositions by means of a universal maximality property. The JSJ decomposition should not be viewed as a tree (which is not uniquely defined) but as a canonical deformation space of trees. We prove that JSJ decompositions of finitely presented groups always exist, without any assumption on edge groups. Many examples are given.

This paper and its companion arXiv:1002.4564 have been replaced by arXiv:1602.05139

References in corpus (3)

• Trees of cylinders and canonical splittings
• JSJ decompositions: definitions, existence, uniqueness. II. Compatibility and acylindricity
• Scott and Swarup's regular neighbourhood as a tree of cylinders

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• JSJ decompositions: definitions, existence, uniqueness. II. Compatibility and acylindricity
• McCool groups of toral relatively hyperbolic groups
• Ampleness in the free group
• A note on ampleness in the theory of non abelian free groups
• Vertex finiteness for splittings of relatively hyperbolic groups
• Test elements in torsion-free hyperbolic groups
• Quasi-isometry Invariants from Decorated Trees of Cylinders of Two-Ended JSJ Decompositions
• Group Actions on Real Cubings and Limit Groups over Partially Commutative Groups