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Journals / Academic Platform Journal of Engineering and Smart Systems / 2026 / Volume: 7 Issue: 2

Dynnikov Coordinates and 𝝅𝟏–Train Tracks

Dynnikov Koordinatları ve 𝝅𝟏–Train Track Grafikleri

Saadet Öykü Yurttas(DİCLE ÜNİVERSİTESİ)0000-0002-0262-1914
Umut Gungorur(DİCLE ÜNİVERSİTESİ)0000-0001-5991-4956
Pages
—
Publication Date
2019-05-25
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

In this paper we introduce.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:A well known way to coordinatize multicurves on a given surface is to use train tracks.
📊
Key Findings & Data: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}.
💡
Conclusion & Impact:In this paper we introduce.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Multicurves · Dynnikov coordinates · 𝜋1–train track coordinates

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.

Özet

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 2 𝑛 −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 𝜋 1–train track grafiği koordinatlarını Dynnikov koordinatlarına bağlayan geçiş formülleri sunulmuştur.

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Cite This Article

Yurttas, S. Ö., Gungorur, U. (2019). Dynnikov Coordinates and 𝝅𝟏–Train Tracks. Academic Platform Journal of Engineering and Smart Systems, Volume: 7 Issue: 2. https://doi.org/10.21541/apjes.480959

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