Fuchsian moduli on a Riemann surface—its Poisson structure and Poincaré-Lefschetz duality
Fuchsian moduli on a Riemann surface—its Poisson structure and Poincaré-Lefschetz duality
复制标题
黎曼曲面上的 Fuchsian 模量——泊松结构和庞加莱-莱夫谢茨对偶性
DOI：
--
复制
发表时间：
1992
期刊：
影响因子：
--
通讯作者：
Katsunori Iwasaki
中科院分区：
文献类型：
--
作者：
Katsunori Iwasaki
闭黎曼曲面上的Fuchsian射影联络的模空间具有Poisson结构。射影单列表示在穿孔黎曼曲面上的模空间也允许Poisson结构，这种结构源于上同调的Poincare-Lefschetz对偶。我们将通过射影单调映射证明前者的泊松结构与后者的拉回重合。这一结果从本质上解释了保单形变产生哈密顿结构的原因
The moduli space of Fuchsian projective connections on a closed Riemann surface admits a Poisson structure. The moduli space of projective monodromy representations on the punctured Riemann surface also admits a Poisson structure which arises from the Poincare-Lefschetz duality for cohomology. We shall show that the former Poisson structure coincides with the pull-back of the latter by the projective monodromy map. This result explains intrinsically why a Hamiltonian structure arises in the monodromy preserving deformation