Instruct: Identify the main and secondary category of Arxiv papers based on the titles
Query: Homology cylinders: an enlargement of the mapping class group
0
The categories of this paper are: hep-ph
12
The categories of this paper are: nucl-th
32
The categories of this paper are: atom-ph
3
The categories of this paper are: physics
23
The categories of this paper are: solv-int
26
The categories of this paper are: bayes-an
27
The categories of this paper are: comp-gas
34
The categories of this paper are: chem-ph
9
The categories of this paper are: nlin
1
The categories of this paper are: cs
18
The categories of this paper are: econ
15
The categories of this paper are: nucl-ex
31
The categories of this paper are: ao-sci
29
The categories of this paper are: funct-an
28
The categories of this paper are: alg-geom
5
The categories of this paper are: gr-qc