标题： 一些小Seifert纤维空间族上的紧接触结构 显示英文标题

标题： Tight contact structures on some families of small Seifert fiber spaces

摘要： 假设 $K$是一个在 3-流形 $Y$中的纽结，并且 $Y$具有一对不同的接触结构。 假设 $K$在这些接触结构中都有勒让德表示，使得相应的托尔森-本尼奎姆框架是等价的。 本文提供了一种方法来证明沿这两个表示进行勒让德手术后得到的接触结构仍然不同。 将这种方法应用于起始流形为 $-\Sigma(2,3,6m+1)$且纽结为奇异纤维的情况，并结合凸面理论，我们可以对某些塞弗特纤维空间上的紧致接触结构进行分类。 显示英文摘要

摘要： Suppose $K$ is a knot in a 3-manifold $Y$, and that $Y$ admits a pair of distinct contact structures. Assume that $K$ has Legendrian representatives in each of these contact structures, such that the corresponding Thurston-Bennequin framings are equivalent. This paper provides a method to prove that the contact structures resulting from Legendrian surgery along these two representatives remain distinct. Applying this method to the situation where the starting manifold is $-\Sigma(2,3,6m+1)$ and the knot is a singular fiber, together with convex surface theory we can classify the tight contact structures on certain families of Seifert fiber spaces.