Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Homotopy types of gauge groups over non-simply-connected closed
  4-manifolds   Let $G$ be a simply-connected simple compact Lie group and let $M$ be an
orientable smooth closed 4-manifold. In this paper we calculate the homotopy
type of the suspension of $M$ and the homotopy types of the gauge groups of
principal $G$-bundles over $M$ when $\pi_1(M)$ is: (1)~$\mathbb{Z}^{*m}$,
(2)~$\mathbb{Z}/p^r\mathbb{Z}$, or
(3)~$\mathbb{Z}^{*m}*(*^n_{j=1}\mathbb{Z}/p_j^{r_j}\mathbb{Z})$, where $p$ and
the $p_j$'s are odd primes.

9
The categories of this paper are: nlin
22
The categories of this paper are: chao-dyn
18
The categories of this paper are: econ
1
The categories of this paper are: cs
14
The categories of this paper are: math-ph
29
The categories of this paper are: funct-an
10
The categories of this paper are: q-bio
7
The categories of this paper are: hep-th
31
The categories of this paper are: ao-sci
37
The categories of this paper are: supr-con
12
The categories of this paper are: nucl-th
30
The categories of this paper are: q-alg
34
The categories of this paper are: chem-ph
5
The categories of this paper are: gr-qc
15
The categories of this paper are: nucl-ex
32
The categories of this paper are: atom-ph