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    Moves on curves on nonorientable surgaces
    (Rocky Mountain Mathematics Consortium, 2022) Atalan, Ferihe; Yurttaş, S. Öykü
    Let Ng,n denote a nonorientable surface of genus g with n punctures and one boundary component. We give an algorithm to calculate the geometric intersection number of an arbitrary multicurve L with so-called relaxed curves in Ng,n making use of measured π1-train tracks. The algorithm proceeds by the repeated application of three moves which take as input the measures of L and produces as output a multicurve L′ which is minimal with respect to each of the relaxed curves. The last step of the algorithm calculates the number of intersections between L′ and the relaxed curves.
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    Öğe
    RELAXING MULTICURVES ON THE TWICE PUNCTURED MÖBIUS BAND
    (Bilal GÜMÜŞ, 2023) Baykal, Abdullah; Atalan, Ferihe; Yurttaş, Saadet Öykü
    Let N1,n (n ? 1) be a non-orientable surface of genus 1 with n punctures and one boundary component. Generalized Dynnikov coordinates provide a bijection between the set of multicurves in N1,n and Z2n-1 \ {0}. In this paper we restrict to the case where n = 2 and describe an algorithm to relax a multicurve in N1,2 making use of its generalized Dynnikov coordinates