Fenchel-Nielsen coordinates of the branch loci of cyclic actions

2025/12/25 by Atreyee Bhattacharya, Bhattacharya, Atreyee, Satyajit Maity +3
Mathematics · #Analytic and geometric function theory #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Holomorphic and Operator Theory #Primary 57K20 #Secondary 57M60

paper · doi:10.48550/arxiv.2512.21463

openalex publication_date 2025/12/25 · openalex created_date 2025/12/30 · openalex updated_date 2026/07/28

Abstract

Let S_g be a closed, connected, and oriented smooth surface of genus g≥ 2. Let the mapping class group of S_g be denoted by Mod(S_g) and the Teichmüller space of S_g by Teich(S_g). It is known that Mod(S_g) acts by isometries on Teich(S_g) with respect to the Weil-Petersson metric. In this paper, we develop algorithms to describe the Fenchel-Nielsen coordinates of fixed points of the actions of certain finite cyclic subgroups of Mod(S_g) on Teich(S_g). As applications of these algorithms, we compute the Fenchel-Nielsen coordinates of the fixed points of three cyclic subgroups of orders 10, 8, and 4, in Mod(S₂).

Citations

• Geometric realizations of cyclic actions on surfaces -- II
• Geometric realizations of cyclic actions on surfaces

Related

• Geometric realizations of cyclic actions on surfaces -- II
• Estimating the distances between hyperbolic structures in the moduli space
• Geometric realizations of cyclic actions on surfaces
• Fenchel-Nielsen Coordinates for Maximal Representations
• Weil-Petersson Completion of Teichmueller Spaces and Mapping Class Group Actions