Parity, Virtual Closure and Minimality of Knotoids
| dc.contributor.author | Güğümcü, Neslihan | |
| dc.contributor.author | Kauffman, Louis H. | |
| dc.date.accessioned | 2022-08-15T18:24:31Z | |
| dc.date.available | 2022-08-15T18:24:31Z | |
| dc.date.issued | 2021 | |
| dc.description.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. | en_US |
| dc.description.sponsorship | The first author's work was supported by the Dorothea Schlozer Postdoctoral Program for Women Scientists by the University of Goettingen. The second author's work was supported by the Laboratory of Topology and Dynamics, Novosibirsk State University (contract no. 14.Y26.31.0025 with the Ministry of Education and Science of the Russian Federation). | en_US |
| dc.identifier.doi | 10.1142/S0218216521500760 | |
| dc.identifier.issn | 0218-2165 | |
| dc.identifier.issn | 1793-6527 | |
| dc.identifier.scopus | 2-s2.0-85124013054 | |
| dc.identifier.uri | https://doi.org/10.1142/S0218216521500760 | |
| dc.identifier.uri | https://hdl.handle.net/11147/12369 | |
| dc.language.iso | en | en_US |
| dc.publisher | World Scientific Publishing | en_US |
| dc.relation.ispartof | Journal of Knot Theory and its Ramifications | en_US |
| dc.rights | info:eu-repo/semantics/closedAccess | en_US |
| dc.subject | Knotoids | en_US |
| dc.subject | Crossing number | en_US |
| dc.subject | Virtual knots | en_US |
| dc.title | Parity, Virtual Closure and Minimality of Knotoids | en_US |
| dc.type | Article | en_US |
| dspace.entity.type | Publication | |
| gdc.author.institutional | Güğümcü, Neslihan | |
| gdc.bip.impulseclass | C4 | |
| gdc.bip.influenceclass | C5 | |
| gdc.bip.popularityclass | C4 | |
| gdc.coar.access | metadata only access | |
| gdc.coar.type | text::journal::journal article | |
| gdc.collaboration.industrial | false | |
| gdc.description.department | İzmir Institute of Technology. Mathematics | en_US |
| gdc.description.issue | 11 | en_US |
| gdc.description.publicationcategory | Makale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanı | en_US |
| gdc.description.scopusquality | Q4 | |
| gdc.description.volume | 30 | en_US |
| gdc.description.wosquality | Q4 | |
| gdc.identifier.openalex | W4206910808 | |
| gdc.identifier.wos | WOS:000751830100003 | |
| gdc.index.type | WoS | |
| gdc.index.type | Scopus | |
| gdc.oaire.diamondjournal | false | |
| gdc.oaire.impulse | 5.0 | |
| gdc.oaire.influence | 3.0101075E-9 | |
| gdc.oaire.isgreen | true | |
| gdc.oaire.popularity | 6.739909E-9 | |
| gdc.oaire.publicfunded | false | |
| gdc.oaire.sciencefields | 0101 mathematics | |
| gdc.oaire.sciencefields | 01 natural sciences | |
| gdc.openalex.collaboration | International | |
| gdc.openalex.fwci | 2.21939118 | |
| gdc.openalex.normalizedpercentile | 0.9 | |
| gdc.openalex.toppercent | TOP 10% | |
| gdc.opencitations.count | 5 | |
| gdc.plumx.mendeley | 2 | |
| gdc.plumx.scopuscites | 9 | |
| gdc.scopus.citedcount | 9 | |
| gdc.wos.citedcount | 7 | |
| relation.isAuthorOfPublication.latestForDiscovery | a327856b-b6a5-41b5-8b2d-c7cf8c78b97d | |
| relation.isOrgUnitOfPublication.latestForDiscovery | 9af2b05f-28ac-4012-8abe-a4dfe192da5e |