Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The symplectic isotopy problem for rational cuspidal curves   We define a suitably tame class of singular symplectic curves in 4-manifolds,
namely those whose singularities are modeled on complex curve singularities. We
study the corresponding symplectic isotopy problem, with a focus on rational
curves with irreducible singularities (rational cuspidal curves) in the complex
projective plane. We prove that every such curve is isotopic to a complex curve
in degrees up to 5, and for curves with one singularity whose link is a torus
knot. Classification results of symplectic isotopy classes rely on
pseudo-holomorphic curves together with a symplectic version of birational
geometry of log pairs and techniques from 4-dimensional topology.

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The categories of this paper are: funct-an
6
The categories of this paper are: astro-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: chao-dyn
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The categories of this paper are: hep-th
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The categories of this paper are: alg-geom
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The categories of this paper are: patt-sol
1
The categories of this paper are: cs
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The categories of this paper are: gr-qc
15
The categories of this paper are: nucl-ex
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The categories of this paper are: supr-con
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The categories of this paper are: chem-ph
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The categories of this paper are: nlin
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The categories of this paper are: hep-ex
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The categories of this paper are: mtrl-th
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The categories of this paper are: econ