Action of the Johnson-Torelli group on representation varieties

William M. Goldman, Eugene Z. Xia

研究成果: Article同行評審

2 引文 斯高帕斯(Scopus)


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.

頁(從 - 到)1449-1457
期刊Proceedings of the American Mathematical Society
出版狀態Published - 2012 4月

All Science Journal Classification (ASJC) codes

  • 數學(全部)
  • 應用數學


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