Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Baumslag-Solitar groups, relative profinite completions and measure
  equivalence rigidity   We introduce an algebraic invariant for aperiodic inclusions of probability
measure preserving equivalence relations. We use this invariant to prove that
every stable orbit equivalence between free pmp actions of direct products of
non-amenable Baumslag-Solitar groups whose canonical subgroup acts
aperiodically forces the number of factors of the products to be the same and
the factors to be isomorphic after permutation. This generalises some of the
results obtained by Kida and moreover provides new measure equivalence rigidity
phenomena for Baumslag-Solitar groups. We also obtain a complete classification
of direct products of relative profinite completions of Baumslag-Solitar
groups, continuing recent work of Elder and Willis.

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The categories of this paper are: quant-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: hep-lat
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The categories of this paper are: math-ph
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The categories of this paper are: stat
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The categories of this paper are: hep-th
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The categories of this paper are: gr-qc
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The categories of this paper are: acc-phys
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The categories of this paper are: astro-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: funct-an
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The categories of this paper are: chem-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: alg-geom
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The categories of this paper are: mtrl-th
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The categories of this paper are: atom-ph