Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the asphericity of a symplectic M3 x S1   An interesting question in symplectic topology, which was posed by C. H.
Taubes, concerns the topology of closed (i.e. compact and without boundary)
connected oriented three dimensional manifolds whose product with a circle
admits a symplectic structure. The only known examples of such manifolds are
those which fiber over a circle. Taubes asked whether these examples are the
only examples of such manifolds. An affirmative answer to Taubes' question
would have the following consequence: any such manifold either is diffeomorphic
to the product of a two-sphere with a circle or is irreducible and aspherical.
In this paper, we prove that this implication holds up to connect sum with a
manifold which admits no proper covering spaces with finite index. It is
pointed out that Thurston's geometrization conjecture and known results in the
theory of three dimensional manifolds imply that such a manifold is a
three-dimensional sphere. Hence, modulo the present conjectural picture of
three-dimensional manifolds, we have shown that the stated consequence of an
affirmative answer to Taubes' question holds.

11
The categories of this paper are: hep-lat
16
The categories of this paper are: stat
23
The categories of this paper are: solv-int
3
The categories of this paper are: physics
21
The categories of this paper are: adap-org
14
The categories of this paper are: math-ph
37
The categories of this paper are: supr-con
29
The categories of this paper are: funct-an
10
The categories of this paper are: q-bio
26
The categories of this paper are: bayes-an
34
The categories of this paper are: chem-ph
22
The categories of this paper are: chao-dyn
12
The categories of this paper are: nucl-th
27
The categories of this paper are: comp-gas
30
The categories of this paper are: q-alg
5
The categories of this paper are: gr-qc