Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A short proof of the H\"older-Poincar\'{e} Duality for
  $L_{p}$-cohomology   We give a short proof of the duality theorem for the reduced $L_p$-cohomology
of a complete oriented Riemannian manifold.

11
The categories of this paper are: hep-lat
33
The categories of this paper are: plasm-ph
4
The categories of this paper are: cond-mat
16
The categories of this paper are: stat
9
The categories of this paper are: nlin
15
The categories of this paper are: nucl-ex
30
The categories of this paper are: q-alg
23
The categories of this paper are: solv-int
6
The categories of this paper are: astro-ph
17
The categories of this paper are: q-fin
0
The categories of this paper are: hep-ph
37
The categories of this paper are: supr-con
22
The categories of this paper are: chao-dyn
21
The categories of this paper are: adap-org
29
The categories of this paper are: funct-an
3
The categories of this paper are: physics