Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Slicing knots in definite 4-manifolds   We study the $\mathbb{CP}^2$-slicing number of knots, i.e. the smallest
$m\geq 0$ such that a knot $K\subseteq S^3$ bounds a properly embedded,
null-homologous disk in a punctured connected sum
$(\#^m\mathbb{CP}^2)^{\times}$. We give a lower bound on the smooth
$\mathbb{CP}^2$-slicing number of a knot in terms of its double branched cover,
and we find knots with arbitrarily large but finite smooth
$\mathbb{CP}^2$-slicing number. We also give an upper bound on the topological
$\mathbb{CP}^2$-slicing number in terms of the Seifert form and find knots for
which the smooth and topological $\mathbb{CP}^2$-slicing numbers are both
finite, nonzero, and distinct.

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The categories of this paper are: cond-mat
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The categories of this paper are: bayes-an
32
The categories of this paper are: atom-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: patt-sol
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The categories of this paper are: gr-qc
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The categories of this paper are: nlin
29
The categories of this paper are: funct-an
37
The categories of this paper are: supr-con
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The categories of this paper are: alg-geom
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The categories of this paper are: dg-ga
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The categories of this paper are: stat
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The categories of this paper are: nucl-th
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The categories of this paper are: chao-dyn
0
The categories of this paper are: hep-ph