Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Taming the pseudoholomorphic beasts in $\mathbb{R}\times(S^1\times S^2)$   For a closed oriented smooth 4-manifold X with $b^2_+(X)>0$, the
Seiberg-Witten invariants are well-defined. Taubes' "SW=Gr" theorem asserts
that if X carries a symplectic form then these invariants are equal to
well-defined counts of pseudoholomorphic curves, Taubes' Gromov invariants. In
the absence of a symplectic form there are still nontrivial closed self-dual
2-forms which vanish along a disjoint union of circles and are symplectic
elsewhere. This paper and its sequel describes well-defined counts of
pseudoholomorphic curves in the complement of the zero-set of such
"near-symplectic" forms, and it is shown that they recover the Seiberg-Witten
invariants (mod 2). This is an extension of Taubes' "SW=Gr" theorem to
non-symplectic 4-manifolds. The main result of this paper asserts the
following. Given a suitable near-symplectic form w, a tubular neighborhood N of
its zero-set, and a generic w-compatible almost complex structure J on X-N,
there are well-defined counts of J-holomorphic curves in a completion of the
symplectic cobordism (X-N, w) which are asymptotic to Reeb orbits on the ends.
They can be packaged together to form "near-symplectic" Gromov invariants as a
function of spin-c structures on X.

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The categories of this paper are: plasm-ph
21
The categories of this paper are: adap-org
25
The categories of this paper are: patt-sol
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The categories of this paper are: dg-ga
4
The categories of this paper are: cond-mat
3
The categories of this paper are: physics
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The categories of this paper are: solv-int
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The categories of this paper are: bayes-an
10
The categories of this paper are: q-bio
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The categories of this paper are: quant-ph
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The categories of this paper are: q-alg
1
The categories of this paper are: cs
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The categories of this paper are: eess
11
The categories of this paper are: hep-lat
6
The categories of this paper are: astro-ph
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The categories of this paper are: supr-con