SavedAdd your journal

Journals / Avrupa Bilim ve Teknoloji Dergisi / 2026 / Sayı: 28 Özel Sayı

Generalized Dynnikov Coordinate System of Measured Foliations

Ölçülen Yapraklanmaların Genelleştirilmiş Dynnikov Koordinat Sistemi

Alev Meral(DİCLE ÜNİVERSİTESİ, FEN FAKÜLTESİ, MATEMATİK BÖLÜMÜ)0000-0002-9838-7906
Pages
437–440
Publication Date
2021-11-30
🏛️Bibliographic metadata and full text access for this article are provided via DergiPark.
DergiPark Record ↗
✨

AI Summary & Key Takeaways

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

More specifically, the generalized Dynnikov coordinate system, which defines a homeomorphism between the space of measured foliations defined on S_n and R^(2n+2) \V_n, where V_n={(a;b;T;c):c ≤0 ve T ≠0}∪{0}, is introduced.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this paper, the generalized Dynnikov coordinates obtained for the integral laminations on an orientable surface S_n of genus 1 with n (n ≥2) punctures and 1 boundary component are extended to the measured foliations defined on the same surface.
📊
Key Findings & Data:In this paper, the generalized Dynnikov coordinates obtained for the integral laminations on an orientable surface S_n of genus 1 with n (n ≥2) punctures and 1 boundary component are extended to the measured foliations defined on the same surface.
💡
Conclusion & Impact:More specifically, the generalized Dynnikov coordinate system, which defines a homeomorphism between the space of measured foliations defined on S_n and R^(2n+2) \V_n, where V_n={(a;b;T;c):c ≤0 ve T ≠0}∪{0}, is introduced.
🔬Design:Araştırma Makalesi
📍Scope:Comprehensive Sample
⚙️Variables:Ölçülen yapraklanma · İntegral laminasyon · Genelleştirilmiş Dynnikov koordinatları

Abstract

In this paper, the generalized Dynnikov coordinates obtained for the integral laminations on an orientable surface S_n of genus 1 with n (n ≥2) punctures and 1 boundary component are extended to the measured foliations defined on the same surface. More specifically, the generalized Dynnikov coordinate system, which defines a homeomorphism between the space of measured foliations defined on S_n and R^(2n+2) \V_n, where V_n={(a;b;T;c):c ≤0 ve T ≠0}∪{0}, is introduced.

Özet

Bu çalışmada, n (n ≥2) adet işaretlenmiş nokta ve 1 adet sınır bileşenine sahip olan, 1 cinsli yönlendirilebilir S_n yüzeyindeki integral laminasyonlar için elde edilen genelleştirilmiş Dynnikov koordinatları, aynı yüzeyde tanımlı ölçülen yapraklanmalara genişletilmiştir. Daha açık olarak, S_n yüzeyinde tanımlı ölçülen yapraklanmaların uzayı ve V_n={(a;b;T;c):c ≤0 ve T ≠0}∪{0} olmak üzere R^(2n+2)\V_n arasında bir homeomorfizm tanımlayan genelleştirilmiş Dynnikov koordinat sistemi tanıtılmıştır.

🔖

Cite This Article

Meral, A. (2021). Generalized Dynnikov Coordinate System of Measured Foliations. Avrupa Bilim ve Teknoloji Dergisi, Sayı: 28 Özel Sayı, 437–440. https://doi.org/10.31590/ejosat.1004314

📄 Full Text PDF Viewer

📄

PDF görüntüleyici hazırlanıyor...

References (6)

  1. Dynnikov, I. (2002). On a Yang-Baxter mapping and the Dehornoy ordering. Uspekhi Mat. Nauk, 57(3(345)), 151-152.
  2. Dehornoy, P. (2008). Efficient solutions to the braid isotopy problem. Discrete Appl. Math., 156(16), 3091-3112.
  3. Dehornoy, P., Dynnikov, I., Rolfsen, D., Wiest, B. (2002). Why are braids orderable?. Panoramas et Syntheses [Panoramas and Syntheses]. Societe Mathematique de France, Paris, 14.
  4. Moussafir, J. (2006). On computing the entropy of braids. Funct. Anal. Other Math., 1, 37-46.
  5. Yurttaş, S. Ö. (2011). Dynnikov coordinates and pseudo-Anosov braids. Doktora tezi, Liverpool Üniversitesi Fen Bilimleri Enstitüsü, Liverpool, 168.
  6. Meral, A. (2021). Dynnikov coordinates on punctured torus. Turkish Journal of Mathematics, 45(2), 661-677.