论文标题
斜率在结歧管边界上的秩序检测
Order-detection of slopes on the boundaries of knot manifolds
论文作者
论文摘要
由L空间猜想的激励，我们研究了结歧管上斜率检测的各种概念。这些概念旨在表征当理性同源性通过沿圆环边界组件粘合紧凑型歧管获得的3个球体具有左定基群，并且当打结歧管的dehn填充有一个可左顺序的基本组时。在Heegaard-loer斜率检测和叶面斜率检测的情况下，我们的发展与现有的结果平行，这导致了几种猜想的结构定理，这些定理将相对的Heegaard-loer同源性以及共同导向的tug落叶与由3-manifold基本基础组支持的一组左订单的边界行为与左侧的边界行为。 3个模型组在实际线路上的行动的动态在我们的构造和证明中起着关键作用。我们的分析导致对此类动作的猜测动态约束，在基础歧管很简单的情况下。
Motivated by the L-space conjecture, we investigate various notions of order-detection of slopes on knot manifolds. These notions are designed to characterise when rational homology 3-spheres obtained by gluing compact manifolds along torus boundary components have left-orderable fundamental groups and when a Dehn filling of a knot manifold has a left-orderable fundamental group. Our developments parallel existing results in the case of Heegaard-Floer slope detection and foliation slope detection, leading to several conjectured structure theorems that connect relative Heegaard-Floer homology and the boundary behaviour of co-oriented taut foliations with the set of left-orders supported by the fundamental group of a 3-manifold. The dynamics of the actions of 3-manifold groups on the real line plays a key role in our constructions and proofs. Our analysis leads to conjectured dynamical constraints on such actions in the case where the underlying manifold is Floer simple.
