Counting curve types

Tarik Aougab (1) , Juan Souto (2)

1 Brown University
2 IRMAR - Institut de Recherche Mathématique de Rennes

Let $S$ be a closed orientable hyperbolic surface, and let $\mathcal{O}(K,S)$ denote the number of mapping class group orbits of curves on $S$ with at most $K$ self-intersections. Building on work of Sapir [16], we give upper and lower bounds for $\mathcal{O}(K,S)$ which are both exponential in $\sqrt{K}$.

Domaines: Topologie géométrique [math.GT]

Tarik Aougab, Juan Souto. Counting curve types. American Journal of Mathematics, 2018, 140 (6), pp.1423-1441. ⟨10.1353/ajm.2018.0043⟩. ⟨hal-01342818⟩