Persona:
Costa González, Antonio Félix

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0000-0002-9905-0264
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Costa González
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Antonio Félix
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2021 - 20244
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Autor: Costa González, Antonio Félix × Fecha de inicio: 2020 ×

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Mostrando 1 - 4 de 4
  • 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
    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
    On the topological type of anticonformal square roots of automorphisms of even order of Riemann surfaces
    (Springer, 2024-06-04) Costa González, Antonio Félix
    Let S be a (compact) Riemann surface of genus greather that one. Two automorphism of S are topologically equivalent if they are conjugated by a homeomorphism. The topological classi cation of automorphisms is a classical problem and its study was initiated by J. Nielsen who in the thirties classi ed conformal ones. The case of anticonformal automorphisms is more involved and was solved by K. Yocoyama in the 80s-90s. In order to decide whether two anti-conformal automorphisms are equivalent, it is usually necessary to take into account many invariants, some of which are di cult to compute. In this work we present some situations where the topological equivalence is mainly due to the genus of some quotient surfaces and the algebraic structure of the automorphism group. An anticonformal square root of a conformal automorphism f is an anticonformal automorphism g such that g2 = f . Let g1 and g2 be anticonformal square roots of the same conformal automorphism of order m, where m is an even integer. If genus of S= hg1; g2i is even and genus of S= hgii is 6= 2 we prove that hg1i and hg2i are topologically equivalent. If genus of S= hg1; g2i is odd and hg1; g2i is abelian we obtain that hg1i and hg2i are topologically equivalent. We give examples to justify the condition genus of S= hgii 6= 2 and hg1; g2i abelian in each case.
  • 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.