Exhausting Curve Complexes by Finite Rigid Sets on Nonorientable Surfaces

Abstract

Let $N$ be a compact, connected, nonorientable surface of genus $g$ with $n$ boundary components. Let $\mathcal{C}(N)$ be the curve complex of $N$. We prove that if $(g,n) = (3,0)$ or $g + n \geq 5$, then there is an exhaustion of $\mathcal{C}(N)$ by a sequence of finite rigid sets. This improves the author's result on exhaustion of $\mathcal{C}(N)$ by a sequence of finite superrigid sets.