Persona:
Costa González, Antonio Félix

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ORCID
0000-0002-9905-0264
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Costa González
Nombre de pila
Antonio Félix
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2021 - 20254
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Nivel de acceso: info:eu-repo/semantics/openAccess × Fecha de inicio: 2020 ×

Resultados de la búsqueda

Mostrando 1 - 4 de 4
  • Miniatura
    Publicación
    Periodic projections of alternating knots
    (2021-08-15) Costa González, Antonio Félix; Quach Honglerb, Cam Van
    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].
  • Miniatura
    Publicación
    One dimensional equisymmetric strata in moduli space with genus 1 quotient surfaces
    (Springer, 2024) S. Allen Broughton; Costa González, Antonio Félix; Izquierdo, Milagros; https://orcid.org/0000-0002-9557-9566
    The complex orbifold structure of the moduli space of Riemann surfaces of genus g (g ≥2) produces a stratification into complex subvarieties named equisymmetric strata. Eachequisymmetric stratum is formed by the surfaces where the group ofautomorphisms acts in a topologically equivalent way. The Riemann surfaces in the equisymmetric strata of dimension one are of two structurally different types. Type 1 equisymmetric strata correspond to Riemann surfaces where the group of automorphisms produces a quotient surface of genus zero, while those of Type 2 appear when such a quotient is a surface of genus one. Type 1 equisymmetric strata have been extensively studied by the authors of the present work in a previous recent paper, we now focus on Type 2 strata. We first establish the existence of such strata and their frequency of occurrence in moduli spaces. As a main result we obtain a complete description of Type 2 strata as coverings of the sphere branched over three point (Belyi curves) and where certain isolated points (punctures) have to be eliminated. Finally, we study in detail the doubly infinite family of Type 2 strata whose automorphism groupshave order the product of two primes.
  • Miniatura
    Publicación
    Periodicity and free periodicity of alternating knots
    (ELSEVIER, 2023-05-16) Costa González, Antonio Félix; Quach Honglerb, Cam Vam
    In 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.
  • Miniatura
    Publicación
    Modular companions in planar one-dimensional equisymmetric strata
    (Universal Wiser, 2025) Costa González, Antonio Félix; Broughton, S. Allen; Izquierdo, Milagros
    Consider, in the moduli space of Riemann surfaces of a fixed genus, the subset of surfaces with non-trivial automorphisms. Of special interest are the numerous subsets of surfaces admitting an action of a given finite group, G, acting with a specific signature. In a previous study [6], we declared two Riemann surfaces to be modular companions if they have topologically equivalent G actions, and that their G quotients are conformally equivalent orbifolds. In this article we present a geometrically-inspired measure to decide whether two modular companions are conformally equivalent (or how different), respecting the G action. Along the way, we construct a moduli space for surfaces with the specified G action and associated equivariant tilings on these surfaces. We specifically apply the ideas to planar, finite group actions whose quotient orbifold is a sphere with four cone points