Publicación:
Periodic projections of alternating knots

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2021-08-15
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Atribución-NoComercial-SinDerivadas 4.0 Internacional
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Resumen
This 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].
Descripción
The 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
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Palabras clave
knot, alternating knot, projection, periodic knot, flype
Citación
Antonio 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.
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Facultad de Ciencias
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Matemáticas Fundamentales
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