Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: What is a Singular Knot?   A singular knot is an immersed circle in $\mathbb R^{3}$ with finitely many
transverse double points. The study of singular knots was initially motivated
by the study of Vassiliev invariants. Namely, singular knots give rise to a
decreasing filtration on the infinite dimensional vector space spanned by
isotopy classes of knots: this is called the Vassiliev filtration, and the
study of the corresponding associated graded space has lead to many insights in
knot theory. The Vassiliev filtration has an alternative, more algebraic
definition for many flavours of knot theory, for example braids and tangles,
but notably not for knots: this view gives rise to connections between knot
theory and quantum algebra. Finally, we review results -- many of them recent
-- on extensions of non-numerical knot invariants to singular knots.

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The categories of this paper are: q-alg
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The categories of this paper are: math-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: astro-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: q-bio
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The categories of this paper are: gr-qc
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The categories of this paper are: patt-sol
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The categories of this paper are: cond-mat
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The categories of this paper are: econ
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The categories of this paper are: chem-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: eess
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The categories of this paper are: ao-sci
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The categories of this paper are: adap-org
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The categories of this paper are: chao-dyn