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Periodicity and free periodicity of alternating knots

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dc.contributor.authorCosta González, Antonio Félix
dc.contributor.authorQuach Honglerb, Cam Vam
dc.date.accessioned2024-06-13T09:41:34Z
dc.date.available2024-06-13T09:41:34Z
dc.date.issued2023-05-16
dc.descriptionThe registered version of this article, first published in “Topology and its Applications", is available online at the publisher's website: Elsevier, https://doi.org/10.1016/j.topol.2023.108582 La versión registrada de este artículo, publicado por primera vez en “Topology and its Applications", está disponible en línea en el sitio web del editor: https://doi.org/10.1016/j.topol.2023.108582
dc.description.abstractIn a previous paper [6], we obtained, as a consequence of Flyping Theorem due to Menasco and Thislethwaite, that the q-periodicity (q>2) of an alternating knot can be visualized in an alternating projection as a rotation of the projection sphere. See also [2]. In this paper, we show that the free q-periodicity (q>2) of an alternating knot can be represented on some alternating projection as a composition of a rotation of order qwith some flypes all occurring on the same twisted band diagram of its essential Conway decomposition. Therefore, for an alternating knot to be freely periodic, its essential decomposition must satisfy certain conditions. We show that any free or non-free q-action is some way visible (virtually visible) and give some sufficient criteria to determine from virtually visible projections the existence of a q-action. Finally, we show how the Murasugi decomposition into atoms as initiated in [12]and [13]enables us to determine the visibility type (q, r)of the freely q-periodic alternating knots ((q, r)-lens knots [3]); in fact, we only need to focus on a certain atom of their Murasugi decomposition to deduce their visibility type.en
dc.description.versionversión publicada
dc.identifier.citationA.F. Costa, C.V.QuachHongler (2023). Periodicity and free periodicity of alternating knots. TopologyanditsApplications, 339 (2023) 108582. https://doi.org/10.1016/j.topol.2023.108582
dc.identifier.doihttps://doi.org/10.1016/j.topol.2023.108582
dc.identifier.issn0166-8641 Online ISSN: 1879-3207
dc.identifier.urihttps://hdl.handle.net/20.500.14468/22633
dc.journal.titleTopology and its Applications
dc.journal.volume339
dc.language.isoen
dc.page.initial108582
dc.publisherELSEVIER
dc.relation.centerFacultad de Ciencias
dc.relation.departmentMatemáticas Fundamentales
dc.rightsAtribución-NoComercial-SinDerivadas 4.0 Internacionales
dc.rights.urihttps://creativecommons.org/licenses/by-nc-nd/4.0/deed.es
dc.subject12 Matemáticas
dc.subject.keywordsperiodicityen
dc.subject.keywordsfree periodicityen
dc.subject.keywordsalternating knoten
dc.titlePeriodicity and free periodicity of alternating knotsen
dc.typeartículoes
dc.typejournal articleen
dspace.entity.typePublication
relation.isAuthorOfPublication8dbf4941-94eb-4e49-a01e-8b9c32463231
relation.isAuthorOfPublication.latestForDiscovery8dbf4941-94eb-4e49-a01e-8b9c32463231
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