Johnson-Torelli群对表示簇的作用
Action of the Johnson-Torelli group on Representation Varieties
摘要：
设B是紧致可定向曲面，具有亏格g和n个边界分量B =（B_1，.，B_n）。令c =（c_1，...，c_n）在[-2，2]^n中。则π的映射类群MCG作用在相对SU（2）-特征标簇X_c：= Hom_C（π，SU（2））/SU（2）上，包含表示ρ的共轭类，其中tr（ρ（B_i））= c_i。该作用在X_c的光滑部分上保持辛结构，且相应的测度是有限的。假设g = 1，n = 2。设J是MCG的子群，它是由Dehn twists沿空同调单环生成的。则J在X_c上的作用对几乎所有c都是遍历的。
英文摘要：
Let Σbe a compact orientable surface with genus g and n boundary components B = (B_1,..., B_n). Let c = (c_1,...,c_n) in [-2,2]^n. Then the mapping class group MCG of Σacts on the relative SU(2)-character variety X_c := Hom_C(π, SU(2))/SU(2), comprising conjugacy classes of representations ρwith tr(ρ(B_i)) = c_i. This action preserves a symplectic structure on the smooth part of X_c, and the corresponding measure is finite. Suppose g = 1 and n = 2. Let J be the subgroup of MCG 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.
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