2022/12/19 by Hyungryul Baik, Baik, Hyungryul, Changsub Kim +1
Computer Science · Mathematics · #37E30 #57M99 #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.2212.09891
openalex publication_date 2022/12/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We show that a pseudo-Anosov map constructed as a product of the large power of Dehn twists of two filling curves always has a geodesic axis on the curve graph of the surface. We also obtain estimates of the stable translation length of a pseudo-Anosov map, when two filling curves are replaced by multicurves. Three main applications of our theorem are the following: (a) determining which word realizes the minimal translation length on the curve graph within a specific class of words, (b) giving a new class of pseudo-Anosov maps optimizing the ratio of stable translation lengths on the curve graph to that on Teichmüller space, (c) giving a partial answer of how much powers will be needed for Dehn twists to generate right-angled Artin subgroup of the mapping class group.