Instruct: Identify the main and secondary category of Arxiv papers based on the titles
Query: A cocyclic construction of $S^1$-equivariant homology and application to
  string topology
31
The categories of this paper are: ao-sci
6
The categories of this paper are: astro-ph
32
The categories of this paper are: atom-ph
14
The categories of this paper are: math-ph
37
The categories of this paper are: supr-con
27
The categories of this paper are: comp-gas
5
The categories of this paper are: gr-qc
3
The categories of this paper are: physics
30
The categories of this paper are: q-alg
11
The categories of this paper are: hep-lat
21
The categories of this paper are: adap-org
16
The categories of this paper are: stat
33
The categories of this paper are: plasm-ph
36
The categories of this paper are: cmp-lg
15
The categories of this paper are: nucl-ex
8
The categories of this paper are: hep-ex