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

Abstract

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

18 pages, 1 figure. Revised version to appear in the journal of "Ergodic Theory and Dynamical Systems"

Cited by in corpus (5)

• Geometry of $\mathrm{SU}(3)$-character varieties of torus knots
• Dynamics on nilpotent character varieties
• Non-ergodicity on SU(2) and SU(3) character varieties of the once-punctured torus
• Mapping class group orbit closures for Deroin-Tholozan representations
• Dynamics on the SU(2,1)-character variety of the one-holed torus