Applications of the Dynnikov coordinate system on the boundary of Teichmüller space

2018/12/31 by S. Öykü Yurttaş, Yurttaş, S. Öykü
Mathematics · #Advanced Combinatorial Mathematics #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.1812.11769

openalex publication_date 2018/12/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The Dynnikov coordinate system puts global coordinates on the boundary of Teichmüller space of an n--punctured disk. We survey the Dynnikov coordinate system, and investigate how we use this coordinate system to study pseudo--Anosov braids making use of results from Thurston's theory on surface homeomorphisms.

Citations

• Train-tracks for surface homeomorphisms

Related

• Dynnikov coordinates on punctured torus
• Black holes in the Dynnikov Coordinate Plane
• Collar parameters for Teichmuller Space & Measured Foliations on a Surface Research Announcement
• On the Kontsevich geometry of the combinatorial Teichmüller space
• Fiber Structure and Local Coordinates for the Teichmueller Space of a Bordered Riemann Surface