Instruct: Identify the main and secondary category of Arxiv papers based on the titles
Query: A homology theory for tropical cycles on integral affine manifolds and a
  perfect pairing
31
The categories of this paper are: ao-sci
35
The categories of this paper are: mtrl-th
8
The categories of this paper are: hep-ex
10
The categories of this paper are: q-bio
32
The categories of this paper are: atom-ph
37
The categories of this paper are: supr-con
20
The categories of this paper are: acc-phys
14
The categories of this paper are: math-ph
16
The categories of this paper are: stat
13
The categories of this paper are: quant-ph
29
The categories of this paper are: funct-an
23
The categories of this paper are: solv-int
3
The categories of this paper are: physics
21
The categories of this paper are: adap-org
0
The categories of this paper are: hep-ph
18
The categories of this paper are: econ