Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Locally holomorphic maps yield symplectic structures   For a smooth map $f:X^4\to\Sigma^2$ that is locally modeled by holomorphic
maps, the domain is shown to admit a symplectic structure that is symplectic on
some regular fiber, if and only if $f^*[\Sigma]\ne0$. If so, the space of
symplectic forms on $X$ that are symplectic on all fibers is nonempty and
contractible. The cohomology classes of these forms vary with the maximum
possible freedom on the reducible fibers, subject to the obvious constraints.
The above results are derived via an analogous theorem for locally holomorphic
maps $f:X^{2n}\to Y^{2n-2}$ with $Y$ symplectic.

9
The categories of this paper are: nlin
6
The categories of this paper are: astro-ph
33
The categories of this paper are: plasm-ph
7
The categories of this paper are: hep-th
31
The categories of this paper are: ao-sci
17
The categories of this paper are: q-fin
18
The categories of this paper are: econ
0
The categories of this paper are: hep-ph
5
The categories of this paper are: gr-qc
11
The categories of this paper are: hep-lat
30
The categories of this paper are: q-alg
21
The categories of this paper are: adap-org
10
The categories of this paper are: q-bio
27
The categories of this paper are: comp-gas
13
The categories of this paper are: quant-ph
23
The categories of this paper are: solv-int