关于瑟斯顿拉回图的秩
On the rank of the Thurston pullback map
摘要：
在适当的假设下，标记$2$ -球面的保向分支覆叠映射在相应的Teichmüller空间之间诱导回拉映射.通过分析作用在可积二次微分上的相应的前推算子，我们得到了拉回映射的导数在标记点上的覆盖作用下的秩的全局下界.在动力学背景下，目标和源中的两组标记点与后临界集重合。调查由此产生的拉回地图的核心部分瑟斯顿的拓扑特征的后临界有限理性地图。具有常数拉回的后临界有限映射已经被许多作者研究过。在这个方向上，我们的方法提供了上界的大小的后临界集的地图与常数拉回，并表明，后临界动态是高度限制。
英文摘要：
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.
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