Action of the Johnson-Torelli group on representation varieties

Let Σ be a compact orientable surface with genus g and n boundary components B = (B1, ..., Bn). Let c = (c ₁, ..., c _n) ∈ [-2, 2] ⁿ. Then the mapping class group MCG of Σ acts on the relative SU(2)-character variety X _CHom _C(π, SU(2))/SU(2), comprising conjugacy classes of representations ρ with tr(ρ(B _i)) = c _i. This action preserves a symplectic structure on the smooth part of XC, and the corresponding measure is finite. Suppose g = 1 and n = 2. Let J ⊂ MCG be the subgroup generated by Dehn twists along null homologous simple loops in Σ. Then the action of J on X _C is ergodic for almost all c.