论文标题
S稳定的叶子在带有横向REEB流动的流量上
S-stable foliations on flow-spines with transverse Reeb flow
论文作者
论文摘要
R. Benedetti和C. petronio引入了分支简单多面体在分支简单多面体上的S稳定性的概念，用于研究3个模型的接触结构的特征性叶子。我们还假设，在分支简单的多面体$ p $上定义叶片的1形$β$满足$dβ> 0 $，这意味着叶面是触点形式的特征性叶面，其reeb流动为$ p $。在本文中，我们表明，如果存在$dβ> 0 $的$ p $上的1形$β$，那么我们可以找到具有相同属性的1形式，并且还具有S稳定。然后，我们证明，在正流或负流量上，S稳定叶片的简单切相点的数量至少为2，并提供了一种配方，用于在鲍鱼上使用$dβ> 0 $构建1型$β$的特征叶面。
The notion of S-stability of foliations on branched simple polyhedrons is introduced by R. Benedetti and C. Petronio in the study of characteristic foliations of contact structures on 3-manifolds. We additionally assume that the 1-form $β$ defining a foliation on a branched simple polyhedron $P$ satisfies $dβ>0$, which means that the foliation is a characteristic foliation of a contact form whose Reeb flow is transverse to $P$. In this paper, we show that if there exists a 1-form $β$ on $P$ with $dβ>0$ then we can find a 1-form with the same property and additionally being S-stable. We then prove that the number of simple tangency points of an S-stable foliation on a positive or negative flow-spine is at least 2 and give a recipe for constructing a characteristic foliation of a 1-form $β$ with $dβ>0$ on the abalone.
