Instruct: Identify the main and secondary category of Arxiv papers based on the titles
Query: On surface subgroups of doubles of free groups
7
The categories of this paper are: hep-th
15
The categories of this paper are: nucl-ex
1
The categories of this paper are: cs
33
The categories of this paper are: plasm-ph
13
The categories of this paper are: quant-ph
22
The categories of this paper are: chao-dyn
29
The categories of this paper are: funct-an
9
The categories of this paper are: nlin
24
The categories of this paper are: dg-ga
25
The categories of this paper are: patt-sol
27
The categories of this paper are: comp-gas
11
The categories of this paper are: hep-lat
19
The categories of this paper are: eess
12
The categories of this paper are: nucl-th
30
The categories of this paper are: q-alg
32
The categories of this paper are: atom-ph