Action of the Johnson-Torelli group on representation varieties

William M. Goldman, Eugene Z. Xia

研究成果: Article同行評審

3 引文 斯高帕斯(Scopus)

摘要

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.

原文English
頁(從 - 到)1449-1457
頁數9
期刊Proceedings of the American Mathematical Society
140
發行號4
DOIs
出版狀態Published - 2012 四月

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

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