Yazar "Yurttaş, S. Öykü" seçeneğine göre listele

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    Counting components of an integral lamination
    (Springer New York LLC, 2017) Yurttaş, S. Öykü; Hall, Toby
    We present an efficient algorithm for calculating the number of components of an integral lamination on an n-punctured disk, given its Dynnikov coordinates. The algorithm requires O(n2M) arithmetic operations, where M is the sum of the absolute values of the Dynnikov coordinates.
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    Curves on non-orientable surfaces and crosscap transpositions
    (MDPI, 2022) Yurttaş, S. Öykü
    Let N-g,N-n be a non-orientable surface of genus g with n punctures and one boundary component. In this paper, we describe multicurves in N-g,N-n making use of generalized Dynnikov coordinates, and give explicit formulae for the action of crosscap transpositions and their inverses on the set of multicurves in N-g,N-n in terms of generalized Dynnikov coordinates. This provides a way to solve on non-orientable surfaces various dynamical and combinatorial problems that arise in the study of mapping class groups and Thurston's theory of surface homeomorphisms, which were solved only on orientable surfaces before.
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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.