The mapping class group action on -character varieties

WILLIAM M. GOLDMAN, SEAN LAWTON, EUGENE Z. XIA
2020 Ergodic Theory and Dynamical Systems  
Let $\unicode[STIX]{x1D6F4}$ be a compact orientable surface of genus $g=1$ with $n=1$ boundary component. The mapping class group $\unicode[STIX]{x1D6E4}$ of $\unicode[STIX]{x1D6F4}$ acts on the $\mathsf{SU}(3)$ -character variety of $\unicode[STIX]{x1D6F4}$ . We show that the action is ergodic with respect to the natural symplectic measure on the character variety.
doi:10.1017/etds.2020.50 fatcat:7ly5fnkrx5afjdfgzatm2mny4i