Maximal Thurston–Bennequin number and reducible Legendrian surgery
Maximal Thurston–Bennequin number and reducible Legendrian surgery
复制标题
最大瑟斯顿-贝内昆数和可简化的勒让德手术
作者：
Kouichi Yasui
我们给出了一个构造$S^{3}中的纽结的Legendrian表示的方法，它在一定条件下实现了其最大的瑟斯顿-本尼金数。该方法利用了$D^{4}$的Stein句柄分解，所得到的Legendrian表示通常非常复杂(相对于拓扑纽结类型的复杂性)。作为应用，我们构造了$S^{3}中的无穷多个纽结，每个纽结在标准紧接触结构中通过Legendrian运算产生一个可约的3-流形。这推翻了Lidman和Sivek的一个猜想。
We give a method for constructing a Legendrian representative of a knot in $S^{3}$ which realizes its maximal Thurston–Bennequin number under a certain condition. The method utilizes Stein handle decompositions of $D^{4}$ , and the resulting Legendrian representative is often very complicated (relative to the complexity of the topological knot type). As an application, we construct infinitely many knots in $S^{3}$ each of which yields a reducible 3-manifold by a Legendrian surgery in the standard tight contact structure. This disproves a conjecture of Lidman and Sivek.