Obstructions to Lagrangian concordance
Obstructions to Lagrangian concordance
复制标题
DOI：
10.2140/agt.2016.16.797
复制
发表时间：
2014-11
期刊：
影响因子：
--
通讯作者：
Christopher R. Cornwell;Lenhard L. Ng;Steven Sivek
中科院分区：
文献类型：
--
作者：
Christopher R. Cornwell;Lenhard L. Ng;Steven Sivek
我们研究了$\mathbb{R}^3$中两个Legendrian纽结之间存在拉格朗日协调的问题。具体地说，就正常规则而言，我们给从任意结到标准的传奇结的和谐设置障碍。我们还对具有去往和来自非纽结的和弦的纽结进行了严格的限制，并从该纽结构造了一个具有不可逆的协和的纽结的无穷族。最后，我们使用我们的障碍来呈现一个完整的纽结列表，其中包含多达14个具有拉格朗日切片的Legendrian代表。
We investigate the question of the existence of a Lagrangian concordance between two Legendrian knots in $\mathbb{R}^3$. In particular, we give obstructions to a concordance from an arbitrary knot to the standard Legendrian unknot, in terms of normal rulings. We also place strong restrictions on knots that have concordances both to and from the unknot and construct an infinite family of knots with non-reversible concordances from the unknot. Finally, we use our obstructions to present a complete list of knots with up to 14 crossings that have Legendrian representatives that are Lagrangian slice.