Right-angled Artin groups and curve graphs of nonorientable surfaces

Abstract

Let $N$ be a closed nonorientable surface with or without marked points. In this paper we prove that, for every finite full subgraph $\Gamma$ of $\mathcal{C}^{\mathrm{two}}(N)$, the right-angled Artin group on $\Gamma$ can be embedded in the mapping class group of $N$. Here, $\mathcal{C}^{\mathrm{two}}(N)$ is the subgraph, induced by essential two-sided simple closed curves in $N$, of the ordinal curve graph $\mathcal{C}(N)$. In addition, we show that there exists a finite graph $\Gamma$ which is not a full subgraph of $\mathcal{C}^{\mathrm{two}}(N)$ for some $N$, but the right-angled Artin group on $\Gamma$ can be embedded in the mapping class group of $N$.