Persona: Costa González, Antonio Félix
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Costa González
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Antonio Félix
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Publicación On the connectedness of the branch locus of moduli space of hyperelliptic Klein surfaces with one boundary(2015-01-01) Izquierdo, Milagros; Costa González, Antonio Félix; Porto Ferreira da Silva, Ana MaríaAbstract. In this work we prove that the hyperelliptic branch locus of ori- entable Klein surfaces of genus g with one boundary component is connected and in the case of non-orientable Klein surfaces it has g+1 2 components, if g is odd, and g+2 2 components for even g. We notice that, for non-orientable Klein surfaces with two boundary components, the hyperelliptic branch loci are connected for all genera.Publicación Periodic projections of alternating knots(2021-08-15) Costa González, Antonio Félix; Quach Honglerb, Cam VanThis 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].Publicación Computing the signatures of subgroups of non-Euclidean crystallographic groups(2017) Cortázar, Ismael; Costa González, Antonio FélixA (planar and cocompact) non-Euclidean crystallographic (NEC) group is a subgroup of the group of (conformal and anti-conformal) isometries of the hyperbolic plane H2 such that H2= is compact. NEC groups are classifed alge- braically by a symbol called signature. In this symbol there is a sign + or and, in the case of sign +, some cycles of integers called period-cycles have an essential direction. In 1990 A.H.M. Hoare gives an algorithm to obtain the signature of a nite index subgroup of an NEC group. The process of Hoare fails in some cases in the task of computing the direction of period-cycles. In this work we complete the algorithm of Hoare, this allows us to construct a program for computing the signature of subgroups of NEC groups in all cases.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/0000-0002-9557-9566The 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.Publicación Periodicity and free periodicity of alternating knots(ELSEVIER, 2023-05-16) Costa González, Antonio Félix; Quach Honglerb, Cam VamIn 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.Publicación Modular companions in planar one-dimensional equisymmetric strata(Universal Wiser, 2025) Costa González, Antonio Félix; Broughton, S. Allen; Izquierdo, MilagrosConsider, 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 pointsPublicación The NSSC (Nec Subgroups Signature Calculation) Package(2017) Cortázar, Ismael; Costa González, Antonio FélixPublicación Congresos, seminarios, reuniones científicas y cursos de verano: 7º Encuentro Internacional sobre E-learning en matemáticas (Oporto, Portugal)(Universidad Nacional de Educación a Distancia (España). Facultad de Ciencias, 2015-01-01) Costa González, Antonio FélixPublicación Entrega de la Medalla de Honor de la UNED a la profesora Milagros Izquierdo, colaboradora habitual de los matemáticos de la Facultad(Universidad Nacional de Educación a Distancia (España). Facultad de Ciencias, 2017-01-01) Costa González, Antonio FélixPublicación Congresos, seminarios, reuniones científicas y cursos de verano: 9º Encuentro e-math 2017(Universidad Nacional de Educación a Distancia (España). Facultad de Ciencias, 2017-01-01) Costa González, Antonio Félix
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