有效映射类群动力学II：几何相交数
Effective mapping class group dynamics II: Geometric intersection numbers
摘要：
我们证明了映射类群在闭曲面的闭曲线空间上的作用在以下意义上有效地跟踪Teichmüller空间上的相应作用：对于除了数量上很少的映射类之外的所有映射类，映射类如何移动Teichmüller空间的给定点的信息确定，直到功率节省误差项，它如何改变给定的闭曲线相对于任意测地线电流的几何相交数。应用包括一个有效的估计描述的速度收敛的Teichmüller测地线的边界在无穷远的Teichmüller空间，一个有效的估计比较Teichmüller和Thurston度量沿映射类群轨道的Teichmüller空间，并在续集，有效的估计计数填充闭测地线封闭，负曲面。
英文摘要：
We show that the action of the mapping class group on the space of closed curves of a closed surface effectively tracks the corresponding action on Teichmüller space in the following sense: for all but quantitatively few mapping classes, the information of how a mapping class moves a given point of Teichmüller space determines, up to a power saving error term, how it changes the geometric intersection numbers of a given closed curve with respect to arbitrary geodesic currents. Applications include an effective estimate describing the speed of convergence of Teichmüller geodesic rays to the boundary at infinity of Teichmüller space, an effective estimate comparing the Teichmüller and Thurston metrics along mapping class group orbits of Teichmüller space, and, in the sequel, effective estimates for countings of filling closed geodesics on closed, negatively curved surfaces.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
