论文标题
批判性固定的反瑟斯顿地图的分类
Classification of critically fixed anti-Thurston maps
论文作者
论文摘要
我们提供了彻底固定的反瑟斯顿地图的完整组合分类，即固定每个临界点的2范围的2秒的逆向分支盖。证明中的第一步，以及一个有趣的结果本身就是与某些平面图关联的“ Schottky Maps”的批判性固定反理性地图的组合分类。这两个分类结果都在很大程度上依赖于瑟斯顿理论的定向反向版本，包括我们在本文中开发的反瑟斯顿地图的规范分解。最后，我们为全球曲线吸引子和扭曲问题提供了一些应用，以及具有对称性的反理性地图和批判性固定的抗多项式图。
We provide a complete combinatorial classification of critically fixed anti-Thurston maps, i.e., orientation-reversing branched covers of the 2-sphere that fix every critical point. The first step in the proof, and an interesting result in its own right, is a combinatorial classification of critically fixed anti-rational maps as "Schottky maps" associated to certain plane graphs. Both of these classification results heavily rely on an orientation-reversing version of Thurstons's theory, including the canonical decomposition of anti-Thurston maps, which we develop in this paper. Lastly, we give some applications to the global curve attractor and twisting problems, as well as to anti-rational maps with symmetries and to critically fixed anti-polynomials.
