Saadet Öykü Yurttaş, Umut Güngörür

Dynnikov Koordinatları ve ??–Train Track Grafikleri

Verilen bir yüzeyde tanımlı çoklu eğrileri koordinatlandırmanın alışılmış bir yolu train track grafiklerini kullanmaktır. Yüzeyin sonlu noktası çıkarılmış ?? diski olması durumunda ise çoklu eğrilerin kümesi ile ℤ 2?−4 {0} arasında birebir ve örten bir dönüşüm veren Dynnikov koordinat sistemi çoklu eğrileri koordinatlandırmak için alternatif ve etkili bir yol sunar. Bu çalışmada, ??’ de verilen bir çoklu eğrinin belirli tipten bir train track grafiği olan ?1–train track grafiği koordinatlarını Dynnikov koordinatlarına bağlayan geçiş formülleri sunulmuştur.

Dynnikov Coordinates and ??–Train Tracks

A well known way to coordinatize multicurves on a given surface is to use train tracks. In the case where the surface is the ?– punctured disk ?? an alternative and efficient way to coordinatize multicurves is achieved by the Dynnikov coordinate system which gives an explicit bijection between the set of multicurves on ?? and ℤ 2?−4 {0}. In this paper we introduce transition formulae between Dynnikov coordinates and the so–called ?1–train track coordinates of a given multicurve on ??.

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