The geometry of moduli space and the mapping class group

该项目的目标是通过辛几何中的现代不变量来发展负截面曲率的闭黎曼流形M的形变理论。我们的方法是以经典的Teichmüler理论和Kleian群理论为基础的。我们计划用M的泛覆盖的测地线空间上的辛结构来代替经典理论中复结构在两个球面上的作用，这个空间总是与n-1维标准球面的余切丛辛同构的。

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.