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.
All Science Journal Classification (ASJC) codes
- Applied Mathematics