Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The H\"older-Poincar\'e Duality for $L_{q,p}$-cohomology   We prove the following version of Poincare duality for reduced
$L_{q,p}$-cohomology: For any $1<q,p<\infty$, the $L_{q,p}$-cohomology of a
Riemannian manifold is in duality with the interior $L_{p',q'}-cohomology for
$1/p+1/p'=1$, $1/q+1/q'=1$.

4
The categories of this paper are: cond-mat
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The categories of this paper are: astro-ph
17
The categories of this paper are: q-fin
14
The categories of this paper are: math-ph
32
The categories of this paper are: atom-ph
0
The categories of this paper are: hep-ph
15
The categories of this paper are: nucl-ex
34
The categories of this paper are: chem-ph
25
The categories of this paper are: patt-sol
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The categories of this paper are: funct-an
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The categories of this paper are: acc-phys
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The categories of this paper are: hep-th
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The categories of this paper are: hep-lat
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The categories of this paper are: chao-dyn
37
The categories of this paper are: supr-con
33
The categories of this paper are: plasm-ph