Parity in Knotoids

Neslihan Gügümcü; Louis Kauffman

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arXiv · 1905.04089

Parity in Knotoids

Neslihan Gügümcü·Louis Kauffman

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Abstract

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.

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BibTeX RIS

Neslihan Gügümcü, Louis Kauffman. 2019-05-10. Parity in Knotoids. https://arxiv.org/abs/1905.04089

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