Parity, virtual closure and minimality of knotoids

N. Gügümcü, L. H. Kauffman

Результат исследования: Научные публикации в периодических изданияхстатьярецензирование

Аннотация

In this paper, we study parity in planar and spherical knotoids in relation to virtual knots. We introduce a planar version of the parity bracket polynomial for planar knotoids. We show that the virtual closure map (a map from the set of knotoids in S2 to the set of virtual knots of genus at most one) is not surjective, by utilizing the surface bracket polynomial of virtual knots. We give specific examples of virtual knots that are not in the image of the virtual closure map. Turaev conjectured that minimal diagrams of knot-type knotoids have zero height. We prove this conjecture by using the results of Nikonov and Manturov induced by parities of virtual knots.

Язык оригиналаанглийский
Номер статьи2150076
ЖурналJournal of Knot Theory and its Ramifications
Том30
Номер выпуска11
DOI
СостояниеОпубликовано - 1 окт 2021

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