Persona: Bujalance García, Emilio
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eb@mat.uned.es
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0000-0002-3407-8936
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Bujalance García
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Emilio
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Publicación Semblanzas de la Medalla Fields: Maryam Mirzajani, primera mujer en recibir una Medalla Fields(Universidad Nacional de Educación a Distancia (España). Facultad de Ciencias, 2015-01-01) Bujalance García, EmilioPublicación Groups of automorphisms of Riemann and Klein surfaces, our joint work with Marston Conder(University of Primorska Press, 2022-06-27) Bujalance García, Emilio; Cirre Torres, Francisco JavierThis work is a survey on the research that we have carried out together with Professor Marston Conder on groups of automorphisms of Riemann and Klein surfaces over the last twenty years.Publicación Fenchel’s conjecture on NEC groups(Springer, 2025-08-20) Bujalance García, Emilio; Cirre Torres, Francisco Javier; Conder, Marston D. E.; Costa González, Antonio Félix; Agencia Estatal de InvestigaciónA classical discovery known as Fenchel's conjecture and proved in the 1950s, shows that every co-compact Fuchsian group has a normal subgroup of finite index isomorphic to the fundamental group of a compact unbordered orientable surface, or in algebraic terms, that has a normal subgroup of finite index that contains no element of finite order other than the identity. In this paper we initiate and make progress on an extension of Fenchel's conjecture by considering the following question: Does every planar non-Euclidean crystallographic group containing transformations that reverse orientation have a normal subgroup of finite index isomorphic to the fundamental group of a compact unbordered non-orientable surface? We answer this question in the affirmative in the case where the orbit space of is a nonorientable surface, and also in the case where this orbit space is a bordered orientable surface of positive genus. In the case where the genus of the quotient is , we have an affirmative answer in many subcases, but the question is still open for others.Publicación Bounds on the orders of groups of automorphisms of a pseudo-real surface of given genus(London Mathematical Society, 2019-11-12) Bujalance García, Emilio; Cirre Torres, Francisco Javier; Conder, Marston D. E.A compact Riemann surface is called pseudo-real if it admits anti-conformal (orientationreversing) automorphisms, but no anti-conformal automorphism of order 2. In this paper, we consider upper bounds on the order of a group G of automorphisms of a pseudo-real surface S of given genus g > 1, in general and for certain special cases. We determine for all g 2 the orders of the largest cyclic group and the largest abelian group of automorphisms of a pseudo-real surface of genus g, containing orientation-reversing elements, and consider the problem of finding similar bounds when the group contains no orientation-reversing elements. For arbitrary groups, we show that if M(g) is the order of the largest group of automorphisms of a pseudo-real surface of genus g, then M(g) 2g for every even g 2, while M(g) 4(g − 1) for every odd g 3, and we prove that the latter bound is sharp for a very large and possibly infinite set of odd values of g 3. We also give the precise values of M(g) for all g between 2 and 128, together with the signatures for the actions of the corresponding groups of largest order.Publicación Premios entregados en el ICM2006(Universidad Nacional de Educación a Distancia (España). Facultad de Ciencias, 2006-01-01) Bujalance García, Emilio; Martínez García, ErnestoPublicación On the existence of groups of automorphisms of compact Riemann and Klein surfaces(American Mathematical Society, 2021-01-01) Bujalance García, Emilio; Cirre Torres, Francisco JavierEach group G of automorphisms of a compact Riemann surface of genus bigger than one can be written as the (finite) quotient G = Γ/Λ for some Fuchsian groups Γ and Λ where Λ is torsion-free. Amongst the natural questions which arise in this situation, this survey article focuses on the following ones. First, which groups can be realized as the full group of all automorphisms of some compact Riemann surface? Second, does every Fuchsian group Γ contain a torsion-free normal subgroup Λ of finite index? Third, for a fixed finite group G, is it possible to characterize all Fuchsian groups Γ containing a torsion-free normal subgroup Λ such that G = Γ/Λ? And fourth, which conditions assure that a group G of automorphisms of a compact Riemann surface is the full group of all its automorphisms? We will consider these topics not only in the setting of compact Riemann surfaces and Fuchsian groups but also in the setting of compact Klein surfaces and non-euclidean crystallographic groups.Publicación El Congreso Mundial de Matemáticos (ICM) y las Medallas concedidas en 2010(Universidad Nacional de Educación a Distancia (España). Facultad de Ciencias, 2010-01-01) Ulecia García, Teresa; Bujalance García, EmilioPublicación Semblanzas: Profesor David Singerman, Medalla de Plata de la UNED(Universidad Nacional de Educación a Distancia (España). Facultad de Ciencias, 2000-01-01) Bujalance García, EmilioPublicación On Riemann surfaces of genus g with 4g automorphisms(2016-04-01) Izquierdo Barrios, Milagros; Bujalance García, Emilio; Costa González, Antonio FélixWe determine, for all genus g 2 the Riemann surfaces of genus g with exactly 4g automorphisms. For g 6= 3; 6; 12; 15 or 30, this sur- faces form a real Riemann surface Fg in the moduli space Mg: the Riemann sphere with three punctures. We obtain the automorphism groups and extended automorphism groups of the surfaces in the fam- ily. Furthermore we determine the topological types of the real forms of real Riemann surfaces in Fg. The set of real Riemann surfaces in Fg consists of three intervals its closure in the Deligne-Mumford com- pacti cation of Mg is a closed Jordan curve. We describe the nodal surfaces that are limits of real Riemann surfaces in Fg.Publicación Abelian Actions on Pseudo-real Riemann Surfaces(Springer, 2023-04-08) Bujalance García, Emilio; Cirre Torres, Francisco Javier; J. RodríguezA compact Riemann surface is called pseudo-real if it admits orientation-reversing automorphisms but none of them has order two. In this paper, we find necessary and sufficient conditions for the existence of an action on a pseudo-real surface of genus g 2 of an abelian group containing orientation-reversing automorphisms. Several consequences are obtained, such as the solution of the minimum genus problem for such abelian actions.