Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The relation between local and global dual pairs   In this note we clarify the relationship between the local and global
definitions of dual pairs in Poisson geometry. It turns out that these are not
equivalent. For the passage from local to global one needs a connected fiber
hypothesis (this is well known), while the converse requires a dimension
condition (which appears not to be known). We also provide examples
illustrating the necessity of the extra conditions.

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The categories of this paper are: solv-int
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The categories of this paper are: eess
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The categories of this paper are: comp-gas
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The categories of this paper are: mtrl-th
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The categories of this paper are: chao-dyn
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The categories of this paper are: hep-lat
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The categories of this paper are: atom-ph
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The categories of this paper are: econ
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The categories of this paper are: bayes-an
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The categories of this paper are: acc-phys
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The categories of this paper are: nlin
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The categories of this paper are: alg-geom
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The categories of this paper are: q-bio
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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: quant-ph