Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: JSJ decompositions and polytopes for two-generator one-relator groups   We provide a direct connection between the $\mathcal{Z}_{\max}$ (or
essential) JSJ decomposition and the Friedl--Tillmann polytope of a hyperbolic
two-generator one-relator group with abelianisation of rank $2$.
  We deduce various structural and algorithmic properties, like the existence
of a quadratic-time algorithm computing the $\mathcal{Z}_{\max}$-JSJ
decomposition of such groups.

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The categories of this paper are: adap-org
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The categories of this paper are: cs
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The categories of this paper are: bayes-an
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The categories of this paper are: plasm-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: solv-int
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The categories of this paper are: dg-ga
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The categories of this paper are: atom-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: q-alg
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The categories of this paper are: alg-geom
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The categories of this paper are: stat
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The categories of this paper are: hep-ph
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The categories of this paper are: math-ph
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The categories of this paper are: eess
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The categories of this paper are: q-bio