Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The extended mapping class group is generated by three symmetries   We prove that the extended mapping class group is generated by three
orientation reversing involutions.

0
The categories of this paper are: hep-ph
6
The categories of this paper are: astro-ph
5
The categories of this paper are: gr-qc
15
The categories of this paper are: nucl-ex
23
The categories of this paper are: solv-int
12
The categories of this paper are: nucl-th
11
The categories of this paper are: hep-lat
18
The categories of this paper are: econ
7
The categories of this paper are: hep-th
37
The categories of this paper are: supr-con
34
The categories of this paper are: chem-ph
1
The categories of this paper are: cs
24
The categories of this paper are: dg-ga
33
The categories of this paper are: plasm-ph
10
The categories of this paper are: q-bio
20
The categories of this paper are: acc-phys