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 $${\mathcal {C}}^{\textrm{two}}(N)$$ , the right-angled Artin group on $$\Gamma $$ can be embedded in the mapping class group of N. Here, $${\mathcal {C}}^{\textrm{two}}(N)$$ is the subgraph, induced by essential two-sided simple closed curves in N, of the ordinary curve graph $${\mathcal {C}}(N)$$ . In addition, we show that there exists a finite graph $$\Gamma $$ which is not a full subgraph of $${\mathcal {C}}^{\textrm{two}}(N)$$ for some N, but the right-angled Artin group on $$\Gamma $$ can be embedded in the mapping class group of N.