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.

该项目的目标是通过辛几何的现代不变量来开发负截面曲率的闭合黎曼流形 M 的变形理论。我们的方法以经典 Teichmüller 理论和 Kleinian 群理论为模型。经典理论中二球面上的复结构可以通过 M 的泛覆盖测地线空间上的辛结构得到。这个空间总是辛同胚的到维度 n-1 的标准球体的余切丛。