Dynnikov Coordinates and 𝝅𝟏–Train Tracks

Year 2019, Volume: 7 Issue: 2, 316 - 323, 25.05.2019

Saadet Öykü Yurttas , Umut Gungorur

https://doi.org/10.21541/apjes.480959

Abstract

A well known way to coordinatize multicurves on a given surface is to use train tracks. In the case where the surface is the 𝑛–
punctured disk 𝐷𝑛 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 𝐷𝑛 and ℤ
2𝑛−4
\{0}. In this paper we introduce.

Keywords

Multicurves, Dynnikov coordinates, 𝜋1–train track coordinates, geometric intersection number

Dynnikov Koordinatları ve 𝝅𝟏–Train Track Grafikleri

Abstract

Verilen bir yüzeyde tanımlı
çoklu eğrileri koordinatlandırmanın alışılmış bir yolu train track grafiklerini
kullanmaktır. Yüzeyin sonlu noktası çıkarılmış 𝐷𝑛 diski olması durumunda ise çoklu eğrilerin
kümesi ile ℤ 2𝑛−4 \{0} arasında birebir ve örten bir dönüşüm
veren Dynnikov koordinat sistemi çoklu eğrileri koordinatlandırmak için
alternatif ve etkili bir yol sunar. Bu çalışmada, 𝐷𝑛’ de verilen bir çoklu eğrinin belirli tipten bir
train track grafiği olan 𝜋1–train track grafiği koordinatlarını Dynnikov koordinatlarına bağlayan
geçiş formülleri sunulmuştur. 

Keywords

Çoklu eğriler, Dynnikov koordinatları, 𝜋.–train track koordinatları

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