A remark on homomorphisms from right-angled Artin groups to mapping class groups

We study rigidity properties of certain homomorphisms from right-angled Artin groups to mapping class groups. As an application, we show that if $\Gamma ?\mathrm{Map}(S)$ is a subgroup that contains some power of every Dehn twist, then any injective homomorphism $\Gamma \to \mathrm{Map}(S)$ is a restriction of an automorphism of $\mathrm{Map}(S)$.