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 $g+n\ge 5$, 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.

19 pages, 13 figures. arXiv admin note: text overlap with arXiv:1903.04926