Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: JSJ decompositions: definitions, existence, uniqueness. I: The JSJ
  deformation space   This paper and its companion arXiv:1002.4564 have been replaced by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.

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The categories of this paper are: acc-phys
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The categories of this paper are: hep-ex
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The categories of this paper are: nucl-ex
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The categories of this paper are: physics
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The categories of this paper are: atom-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: q-alg
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The categories of this paper are: chem-ph
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The categories of this paper are: hep-th
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The categories of this paper are: plasm-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: ao-sci
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The categories of this paper are: adap-org
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The categories of this paper are: math-ph
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The categories of this paper are: eess