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|Title:||Parity, virtual closure and minimality of knotoids||Authors:||Güğümcü, Neslihan
Kauffman, Louis H.
|Issue Date:||2021||Publisher:||World Scientific Publishing||Abstract:||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 S-2 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.||URI:||https://doi.org/10.1142/S0218216521500760
|Appears in Collections:||Mathematics / Matematik|
Scopus İndeksli Yayınlar Koleksiyonu / Scopus Indexed Publications Collection
WoS İndeksli Yayınlar Koleksiyonu / WoS Indexed Publications Collection
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