Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On virtual embeddings of braid groups into mapping class groups of
  surfaces   In this article, we give a necessary and sufficient condition for embedding a
finite index subgroup of Artin's braid group into the mapping class group of a
connected orientable surface.

21
The categories of this paper are: adap-org
11
The categories of this paper are: hep-lat
0
The categories of this paper are: hep-ph
9
The categories of this paper are: nlin
1
The categories of this paper are: cs
8
The categories of this paper are: hep-ex
20
The categories of this paper are: acc-phys
27
The categories of this paper are: comp-gas
22
The categories of this paper are: chao-dyn
34
The categories of this paper are: chem-ph
36
The categories of this paper are: cmp-lg
12
The categories of this paper are: nucl-th
23
The categories of this paper are: solv-int
6
The categories of this paper are: astro-ph
15
The categories of this paper are: nucl-ex
32
The categories of this paper are: atom-ph