Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Parity in Knotoids   This paper investigates the parity concept in knotoids in $S^2$ and in
$\mathbb{R}^2$ in relation with virtual knots. We show that the virtual closure
map is not surjective and give specific examples of virtual knots that are not
in the image. We introduce a planar version of the parity bracket polynomial
for knotoids in $\mathbb{R}^2$. By using the Nikonov/Manturov theorem on
minimal diagrams of virtual knots we prove a conjecture of Turaev showing that
minimal diagrams of knot-type knotoids have zero height.

3
The categories of this paper are: physics
34
The categories of this paper are: chem-ph
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The categories of this paper are: hep-th
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The categories of this paper are: econ
10
The categories of this paper are: q-bio
37
The categories of this paper are: supr-con
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The categories of this paper are: plasm-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: cond-mat
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The categories of this paper are: acc-phys
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The categories of this paper are: hep-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: quant-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: bayes-an
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The categories of this paper are: comp-gas