The mapping class group action on SU(3)-character varieties

Let $\mathrm{\Sigma }$ be a compact orientable surface of genus $g=1$ with $n=1$ boundary component. The mapping class group $\mathrm{\Gamma }$ of $\mathrm{\Sigma }$ acts on the SU(3)-character variety of $\mathrm{\Sigma }$. We show that the action is ergodic with respect to the natural symplectic measure on the character variety.