Costa González, Antonio FélixQuach Honglerb, Cam Van2024-06-142024-06-142021-08-15Antonio 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.2021.107753.0166-8641 Online ISSN: 1879-3207https://doi.org/10.1016/j.topol.2021.107753https://hdl.handle.net/20.500.14468/22643The 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.2021.107753This 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].eninfo:eu-repo/semantics/openAccess12 Matemáticasjournal articleknotalternating knotprojectionperiodic knotflype