2004/02/02 by Vladimir Turaev, Turaev, Vladimir
Computer Science · Mathematics · #57M20 #Advanced Combinatorial Mathematics #Combinatorics (math.CO) #FOS: Mathematics #Geometric Topology (math.GT) #Mathematical Dynamics and Fractals #Topological and Geometric Data Analysis #math.CO #math.GT #msc:57M20
paper · pdf · doi:10.48550/arxiv.math/0402012
20 pages, no figures. In the third version I extended the introduction and added sections on relations to Grothendieck dessins d'enfants, Riemann surfaces, knots in 3-manifolds, and Coxeter groups of type B
openalex publication_date 2004/02/02 · arxiv created 2004/03/10 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We give a combinatorial description of closed curves on oriented surfaces in terms of certain permutations, called charts. We describe automorphisms of curves in terms of charts and compute the total number of curves counted with appropriate weights. We also discuss relations between curves, Grothendieck dessins d'enfants, Riemann surfaces, Coxeter groups, and words.