The geometry of moduli space and the mapping class group

模空间的几何与映射类群

• 批准号: 5407045
• 负责人: Professorin Dr. Ursula Hamenstädt
• 金额: --
• 依托单位: Mathematisches Institut (MI)
• 依托单位国家: 德国
• 项目类别: Priority Programmes
• 财政年份: 2003
• 资助国家: 德国
• 起止时间: 2002-12-31 至 2010-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/5407045?language=en
• 关键词: geometry; moduli; space; mapping; class

The goal of the project is to develop a deformation theory for closed Riemannian manifolds M of negative sectional curvature via modern invariants from symplectic geometry. Our approach is modeled on classical Teichmüller theory and the theory of Kleinian groups. We plan to replace the role of the complex structure on the two-sphere in the classical theory by the symplectic structure on the space of geodesics of the universal covering of M. This space is always symplectomorphic to the cotangent bundle of the standard sphere of dimension n-1.

该项目的目的是通过对称几何形状的现代不变式为封闭的riemannian歧管开发一种变形理论。我们的方法以经典的Teichmüller理论和克莱恩群体理论为基础。我们计划通过对称结构在M. M.通用覆盖物的大地质学空间中代替经典理论中的复杂结构的作用。该空间始终与维度N-1标准领域的cotangengent bunce键相吻合。