Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Some refined higher type adjunction inequalities on 4-manifolds   We further sharpen higher type adjunction inequalities of P. Ozsv\'ath and Z.
Szab\'o on a 4-manifold $M$ with a nonzero Seiberg-Witten invariant for a
Spin$^c$ structure $\frak{s}$, when an embedded surface $\Sigma\subset M$
satisfies $[\Sigma]\cdot [\Sigma]\geq 0$ and $$|\langle
[\Sigma],c_1(\frak{s})\rangle|+[\Sigma]\cdot [\Sigma]\geq 2b_1(M).$$

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The categories of this paper are: astro-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: math-ph
3
The categories of this paper are: physics
19
The categories of this paper are: eess
33
The categories of this paper are: plasm-ph
29
The categories of this paper are: funct-an
31
The categories of this paper are: ao-sci
36
The categories of this paper are: cmp-lg
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The categories of this paper are: hep-th
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The categories of this paper are: supr-con
32
The categories of this paper are: atom-ph
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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: hep-ex
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The categories of this paper are: q-fin