ACTION OF THE JOHNSON-TORELLI GROUP ON REPRESENTATION VARIETIES

作者：Goldman William M^*; Xia Eugene Z

来源：Proceedings of the American Mathematical Society, 2012, 140(4): 1449-1457.

DOI：10.1090/S0002-9939-2011-10972-9

Let Sigma be a compact orientable surface with genus g and n boundary components B = (B-1, . . . , B-n). Let c= (c(1), . . . , c(n)) epsilon [-2, 2](n).Then the mapping class group MCG of Sigma acts on the relative SU(2)-character variety chi(C) := Hom(C) SU(2))/SU(2), comprising conjugacy classes of representations p with tr(p(B)) = c. This action preserves a symplectic structure on the smooth part of..tc, and the corresponding measure is finite. Suppose g = 1 and n = 2. Let J subset of MCG be the subgroup generated by Dehn twists along null homologous simple loops in E.

• 出版日期2012-4