Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Local solution to the $G_{2}-$monopole equation with prescribed tangent
  cone and $G_{2}-$structure   For any locally defined $G_{2}-$structure and Hermitian-Yang-Mills connection
on $S^{6}$, the $G_{2}-$monopole equation always admits a local solution that
is asymptotic to the HYM-connection.

24
The categories of this paper are: dg-ga
30
The categories of this paper are: q-alg
32
The categories of this paper are: atom-ph
23
The categories of this paper are: solv-int
16
The categories of this paper are: stat
28
The categories of this paper are: alg-geom
8
The categories of this paper are: hep-ex
13
The categories of this paper are: quant-ph
3
The categories of this paper are: physics
31
The categories of this paper are: ao-sci
6
The categories of this paper are: astro-ph
9
The categories of this paper are: nlin
18
The categories of this paper are: econ
36
The categories of this paper are: cmp-lg
37
The categories of this paper are: supr-con
19
The categories of this paper are: eess