TY - JOUR
T1 - Action of the Johnson-Torelli group on representation varieties
AU - Goldman, William M.
AU - Xia, Eugene Z.
PY - 2012/4
Y1 - 2012/4
N2 - 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.
AB - 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.
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U2 - 10.1090/S0002-9939-2011-10972-9
DO - 10.1090/S0002-9939-2011-10972-9
M3 - Article
AN - SCOPUS:84856989385
SN - 0002-9939
VL - 140
SP - 1449
EP - 1457
JO - Proceedings of the American Mathematical Society
JF - Proceedings of the American Mathematical Society
IS - 4
ER -