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Periodic projections of alternating knots

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dc.contributor.authorCosta González, Antonio Félix
dc.contributor.authorQuach Honglerb, Cam Van
dc.date.accessioned2024-06-14T07:18:43Z
dc.date.available2024-06-14T07:18:43Z
dc.date.issued2021-08-15
dc.descriptionThe registered version of this article, first published in “Topology and its Applications, Volume 300, 2021, 107753", is available online at the publisher's website: Elsevier, https://doi.org/10.1016/j.topol.2021.107753 La versión registrada de este artículo, publicado por primera vez en “Topology and its Applications, Volume 300, 2021, 107753", está disponible en línea en el sitio web del editor: Elsevier, https://doi.org/10.1016/j.topol.2021.107753
dc.description.abstractThis paper is devoted to the proof of existence of q-periodic alternating projections of prime alternating q-periodic knots. The main tool is the Menasco-Thistlethwaite’s Flyping Theorem. Let Kbe an oriented prime alternating knot that is q-periodic with q≥3, i.e. that admits a rotation of order qas a symmetry. Then Khas an alternating projection Π(K)such that the rotational symmetry of Kis visualized as a rotation of the projection sphere leaving Π(K)invariant. As an application, we obtain that the crossing number of a q-periodic alternating knot with q≥3is a multiple of q. Furthermore we give an elementary proof that the knot 12a634is not 3-periodic; our proof does not depend on computer calculations as in [11].en
dc.description.versionversión publicada
dc.identifier.citationAntonio F. Costa, Cam Van Quach-Hongler, Periodic projections of alternating knots, Topology and its Applications, Volume 300, 2021, 107753, ISSN 0166-8641, https://doi.org/10.1016/j.topol.2021.107753.
dc.identifier.doihttps://doi.org/10.1016/j.topol.2021.107753
dc.identifier.issn0166-8641 Online ISSN: 1879-3207
dc.identifier.urihttps://hdl.handle.net/20.500.14468/22643
dc.journal.titleTopology and its Applications
dc.journal.volume300
dc.language.isoen
dc.page.initial107753
dc.relation.centerFacultad de Ciencias
dc.relation.departmentMatemáticas Fundamentales
dc.rightsinfo:eu-repo/semantics/openAccess
dc.rights.urihttps://creativecommons.org/licenses/by-nc-nd/4.0/deed.es
dc.subject12 Matemáticas
dc.subject.keywordsknoten
dc.subject.keywordsalternating knoten
dc.subject.keywordsprojectionen
dc.subject.keywordsperiodic knoten
dc.subject.keywordsflypeen
dc.titlePeriodic projections of alternating knotsen
dc.typejournal articleen
dc.typeartículoes
dspace.entity.typePublication
relation.isAuthorOfPublication8dbf4941-94eb-4e49-a01e-8b9c32463231
relation.isAuthorOfPublication.latestForDiscovery8dbf4941-94eb-4e49-a01e-8b9c32463231
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