论文标题
横向通用结的存在
The existence of a transverse universal knot
论文作者
论文摘要
我们证明，有一个结$ k $横向到$ξ_{std} $，紧密的接触结构为$ s^3 $，因此每个触点3- manifold $（m，ξ）$可以作为覆盖沿$ k $的分支的联系人获得。通过联系覆盖，我们的意思是$ k $分支的地图$φ：m \至s^3 $，因此$ξ$是$ξ_{std} $在$φ$下提升的同位素。
We prove that there is a knot $K$ transverse to $ξ_{std}$, the tight contact structure of $S^3$, such that every contact 3-manifold $(M, ξ)$ can be obtained as a contact covering branched along $K$. By contact covering we mean a map $φ: M \to S^3$ branched along $K$ such that $ξ$ is contact isotopic to the lifting of $ξ_{std}$ under $φ$.
