Ergodic theory on moduli spaces

• 成果类型: Article
• 署名作者: Goldman, WM
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.2307/2952454
• 发表日期: 1997
• 页码: 475-507
• 关键词: flat connections; riemann surface; REPRESENTATIONS; CURVES; trees

摘要

Let M be a compact surface with chi(M) < 0 and let G be a compact Lie group whose Levi factor is a product of groups locally isomorphic to SU(2) (for example SU(2) itself). Then the mapping class group Gamma(M) of M acts on the moduli space X(M) of flat G-bundles over M (possibly twisted by a fixed central element of G). When M is closed, then Gamma(M) preserves a symplectic structure on X(M) which has finite total volume on M. More generally, the subspase of X(nl) corresponding to flat bundles with fixed behavior over partial derivative M carries a Gamma(M)-invariant symplectic structure. The main result is that Gamma(M) acts ergodically on X(M) with respect to the measure induced by the symplectic structure.