论文标题
在Thurston撤回地图的等级
On the rank of the Thurston pullback map
论文作者
论文摘要
在某些温和的假设下，标记为$ 2 $ -SPHERES的定向覆盖图覆盖图可引起相应的Teichmüller空间之间的回溯图。通过分析作用于集成二次差速器的相关推动操作员，我们根据封面对标记点的作用而获得了回调映射衍生物衍生物等级的全局下限。在动态环境中，目标中的两组标记点和源与后临界集合一致。研究所得的回调图是瑟斯顿对后有限理性图的拓扑表征的中心部分。各种作者已经研究了有限的有限图。在这个方向上，我们的方法在地图的后临界集合的大小上以恒定的回调提供了上限，并表明后临界动力学受到高度限制。
Under some mild assumptions, an orientation-preserving branched covering map of marked $2$-spheres induces a pullback map between the corresponding Teichmüller spaces. By analyzing the associated pushforward operator acting on integrable quadratic differentials, we obtain a global lower bound on the rank of the derivative of the pullback map in terms of the action of the cover on the marked points. In the dynamical context, the two sets of marked points in the target and source coincide with the postcritical set. Investigating the resulting pullback map is the central part of Thurston's topological characterization of postcritically finite rational maps. Postcritically finite maps with constant pullback have been studied by various authors. In that direction, our approach provides upper bounds on the size of the postcritical set of a map with constant pullback, and shows that the postcritical dynamics is highly restricted.
