Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Twisted Poincar\'{e} duality between Poisson homology and Poisson
  cohomology   A version of the twisted Poincar\'{e} duality is proved between the Poisson
homology and cohomology of a polynomial Poisson algebra with values in an
arbitrary Poisson module. The duality is achieved by twisting the Poisson
module structure in a canonical way, which is constructed from the modular
derivation. In the case that the Poisson structure is unimodular, the twisted
Poincar\'{e} duality reduces to the Poincar\'{e} duality in the usual sense.
The main result generalizes the work of Launois-Richard \cite{LR} for the
quadratic Poisson structures and Zhu \cite{Zhu} for the linear Poisson
structures.

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The categories of this paper are: gr-qc
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The categories of this paper are: patt-sol
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The categories of this paper are: econ
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The categories of this paper are: eess
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The categories of this paper are: q-fin
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The categories of this paper are: solv-int
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The categories of this paper are: hep-ph
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The categories of this paper are: chao-dyn
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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: physics
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The categories of this paper are: quant-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: astro-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: acc-phys