165 research outputs found

    Equivelar and d-Covered Triangulations of Surfaces. I

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    We survey basic properties and bounds for qq-equivelar and dd-covered triangulations of closed surfaces. Included in the survey is a list of the known sources for qq-equivelar and dd-covered triangulations. We identify all orientable and non-orientable surfaces MM of Euler characteristic 0>χ(M)≥−2300>\chi(M)\geq -230 which admit non-neighborly qq-equivelar triangulations with equality in the upper bound q≤⌊12(5+49−24χ(M))⌋q\leq\Bigl\lfloor\tfrac{1}{2}(5+\sqrt{49-24\chi (M)})\Bigl\rfloor. These examples give rise to dd-covered triangulations with equality in the upper bound d≤2⌊12(5+49−24χ(M))⌋d\leq2\Bigl\lfloor\tfrac{1}{2}(5+\sqrt{49-24\chi (M)})\Bigl\rfloor. A generalization of Ringel's cyclic 7mod127{\rm mod}12 series of neighborly orientable triangulations to a two-parameter family of cyclic orientable triangulations Rk,nR_{k,n}, k≥0k\geq 0, n≥7+12kn\geq 7+12k, is the main result of this paper. In particular, the two infinite subseries Rk,7+12k+1R_{k,7+12k+1} and Rk,7+12k+2R_{k,7+12k+2}, k≥1k\geq 1, provide non-neighborly examples with equality for the upper bound for qq as well as derived examples with equality for the upper bound for dd.Comment: 21 pages, 4 figure

    The homotopy theory of polyhedral products associated with flag complexes

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    If KK is a simplicial complex on mm vertices the flagification of KK is the minimal flag complex KfK^f on the same vertex set that contains KK. Letting LL be the set of vertices, there is a sequence of simplicial inclusions L→K→KfL\to K\to K^f. This induces a sequence of maps of polyhedral products (X‾,A‾)L⟶g(X‾,A‾)K⟶f(X‾,A‾)Kf(\underline X,\underline A)^L\stackrel g\longrightarrow(\underline X,\underline A)^K\stackrel f\longrightarrow (\underline X,\underline A)^{K^f}. We show that Ωf\Omega f and Ωf∘Ωg\Omega f\circ\Omega g have right homotopy inverses and draw consequences. For a flag complex KK the polyhedral product of the form (CY‾,Y‾)K(\underline{CY},\underline Y)^K is a co-HH-space if and only if the 11-skeleton of KK is a chordal graph, and we deduce that the maps ff and f∘gf\circ g have right homotopy inverses in this case.Comment: 25 page

    Métriques polyèdrales sur les bords de variétés hyperboliques convexes et flexibilité des polyèdres hyperboliques

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    Cette thèse de doctorat contient trois résultats principaux. Dans le premier chapitre on construit un polyèdre infinitésimalement flexible dans l'espace hyperbolique à trois dimensions dont le volume n'est pas stationnaire sous sa flexion infinitésimale. Dans le deuxième chapitre on obtient une condition nécessaire de flexibilité des suspensions dans l'espace hyperbolique à trois dimensions. Dans les deux derniers chapitres on démontre l'existence d'une variété quasi-Fuchsienne convexe compacte dont la métrique induite de son bord est une métrique polyèdrale hyperbolique prescrite.This thesis contains three main results. In the first chapter we construct an infinitesimally flexible polyhedron in hyperbolic 3-space such that its volume is not stationary under the infinitesimal flex. In the second chapter we obtain a necessary condition for flexibility of suspensions in hyperbolic 3-space. In the last two chapters we show the existence of a quasi-Fuchsian convex compact manifold such that the induced metric on its boundary coincides with a prescribed hyperbolic polyhedral metric

    Three cocluded insect viruses : a biophysical and biological study of the nuclear-polyhedrosis virus of Colias electo, the granulosis virus of Heliothis armigera and the nuclear-polyhedrosis virus of Heliothis zea

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    An investigation was undertaken in some detail of three virus strains of insect pests of agricultural importance, viz. a nuclear-polyhedrosis virus of the lucerne caterpillar, Colias electo, and a granulosis virus of the bollworm, Heliothis armigera, both found in South Africa, and a nuclear-polyhedrosis virus of the bollworm, Heliothis zea, isolated in America, with a view to ascertaining a knowledge of some of the fundamental properties and basic biology of these infective agents. On the basis of the information gained the viruses could be differentiated and their broad classification was established. The morphology of the polyhedra, capsules and virus particles observed by light and electron microscopy has been completed and measurements of the viral elements have been made. Some biophysical properties of the virus particles and their inclusion bodies were recorded, i.e. their resistance to chemical and physical treatments and their relative mobility in an electric field under standard conditions. Observations were made on procedures which brought about varying degrees of purification and concentration of the virus particles from putrefying larvae and the most successful of these were found to be reproducible. They involved the purification of the inclusion bodies and their digestion by weak alkali to release the virus particles. Both preparations of the viral elements were further purified by zone electrophoresis in sucrose density gradients. Some information was gathered on the mode of transmission of the infection from insect to insect by contact or cannibalism, from one generation to the next through the eggs, and particularly from one area to another by virus survival in avian faeces. The incidence and rate of the infection in the larvae was increased by environmental changes such as raising the temperature and also to some extent by spraying with a suspension of endospores of Bacillus thuringiensis. Exposure to other stress conditions was not successful in initiating a fatal infection in the insects. Of particular interest, however, was the observation that by injecting a 'foreign' virus a fatal infection was induced by activation of a native occult virus in the larvae of the silkworm, Bornbyx mori. In the context of the possible application of these infective agents to future methods of biological control of economically disastrous pests, these preliminary experiments were not unrewarding
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