Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Circle bundles over 4-manifolds   Every 1-connected topological 4-manifold M admits a $S^{1}$-covering by
$#_{r-1}S^{2}\times S^{3}$, where $r=$rank$H^{2}(M;\QTR{Bbb}{Z})$.

23
The categories of this paper are: solv-int
9
The categories of this paper are: nlin
20
The categories of this paper are: acc-phys
7
The categories of this paper are: hep-th
18
The categories of this paper are: econ
21
The categories of this paper are: adap-org
0
The categories of this paper are: hep-ph
28
The categories of this paper are: alg-geom
5
The categories of this paper are: gr-qc
17
The categories of this paper are: q-fin
37
The categories of this paper are: supr-con
34
The categories of this paper are: chem-ph
3
The categories of this paper are: physics
4
The categories of this paper are: cond-mat
22
The categories of this paper are: chao-dyn
1
The categories of this paper are: cs