论文标题
周期性的表面同态和接触结构
Periodic Surface Homeomorphisms and Contact Structures
论文作者
论文摘要
周期性的表面自杀（差异）在表面同态的Nielsen-Thurston分类中起着重要作用。可以通过使用组合对象的数据集来描述（结合）周期性的表面同态。在本文中，我们首先将一本理性的开放书与给定数据集（称为标记数据集）的稍作修改关联。众所周知，每本理性的开放书都支持接触结构。因此，我们可以将触点结构与周期地图相关联，并根据标记数据集的组合条件来研究其特性。 特别是，我们证明，一类数据集满足易于检查的组合假设，会产生Stein填充的接触结构。除上述内容外，我们还证明了莫里（Mori）为理性开放书籍的明确构造填充的类似物。我们还证明，像Giroux和Loi-Piergallini的结果一样，可以使理性开放书籍的坦率填补有理性的开放书籍。
Periodic surface homemorphisms (diffeomorphisms) play a significant role in the the Nielsen-Thurston classification of surface homeomorphisms. Periodic surface homeomorphisms can be described (up to conjugacy) by using data sets which are combinatorial objects. In this article, we start by associating a rational open book to a slight modification of a given data set, called marked data set. It is known that every rational open book supports a contact structure. Thus, we can associate a contact structure to a periodic map and study the properties of it in terms combinatorial conditions on marked data sets. In particular, we prove that a class of data sets, satisfying easy-to-check combinatorial hypothesis, gives rise to Stein fillable contact structures. In addition to the above, we prove an analogue of Mori's construction of explicit symplectic filling for rational open books. We also prove a sufficient condition for Stein fillability of rational open books analogous to the positivity of monodromy in honest open books as in the result of Giroux and Loi-Piergallini.
