Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Existence of Symplectic Surfaces   In this paper we show that every degree 2 homology class of a 2n-dimensional
symplectic manifold is represented by an immersed symplectic surface if it has
positive symplectic area. Moreover, the symplectic surface can be chosen to be
embedded if 2n is at least 6. We also analyze the additional conditions under
which embedded symplectic representatives exist in dimension 4.

16
The categories of this paper are: stat
23
The categories of this paper are: solv-int
36
The categories of this paper are: cmp-lg
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The categories of this paper are: alg-geom
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The categories of this paper are: q-fin
32
The categories of this paper are: atom-ph
14
The categories of this paper are: math-ph
7
The categories of this paper are: hep-th
35
The categories of this paper are: mtrl-th
5
The categories of this paper are: gr-qc
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The categories of this paper are: nucl-th
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The categories of this paper are: supr-con
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The categories of this paper are: nucl-ex
3
The categories of this paper are: physics
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The categories of this paper are: adap-org
26
The categories of this paper are: bayes-an