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

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

2009-11-16

arxiv.org/abs/0911.3173v2

Mathematics

Group Theory

Small changes in the paper organisation. 30 pages

Scientific paper

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.

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