On the spectrum of the number of geodesics and tight geodesics in the curve complex

Ryo Matsuda, Kanako Oie, Hiroshige Shiga

Let $S$ be an oriented surface of type $(g,n)$. We are interested in geodesics in the curve complex $\mathcal{C}(S)$ of $S$. In general, two $0$-simplexes in $\mathcal{C}(S)$ have i…