82 research outputs found

    Universal Tessellations

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    Commentary on Robert Riley's article "A personal account of the discovery of hyperbolic structures on some knot complements"

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    We give some background and biographical commentary on the postumous article that appears in this [journal issue | ArXiv] by Robert Riley on his part of the early history of hyperbolic structures on some compact 3-manifolds. A complete list of Riley's publications appears at the end of the article.Comment: 5 page

    Symmetries of quasiplatonic Riemann surfaces

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    We state and prove a corrected version of a theorem of Singerman, which relates the existence of symmetries (anticonformal involutions) of a quasiplatonic Riemann surface S\mathcal S (one uniformised by a normal subgroup NN of finite index in a cocompact triangle group Δ\Delta) to the properties of the group G=Δ/NG=\Delta/N. We give examples to illustrate the revised necessary and sufficient conditions for the existence of symmetries, and we relate them to properties of the associated dessins d'enfants, or hypermaps

    Non-maximal cyclic group actions on compact Riemann surface

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