论文标题
Legendrian接触同源物，用于将链接连接到更高维度的次临界Weinstein歧管
Legendrian contact homology for attaching links in higher dimensional subcritical Weinstein manifolds
论文作者
论文摘要
令$λ$为Legendrian Spheres的链接，在$ 2N $二维的Weinstein歧管$ x $的边界处。我们表明，在一些几何假设下，可以将$λ$的legendrian接触同源性计算减少为1--季节空间中Legendrian接触同源性的计算。由于对1-jet空间的Legendrian接触同源性进行了充分的研究，因此提供了一种简化的方法来计算$λ$的Legendrian接触同源性。当$ x $的亚临界手柄的附件球形不相互作用时，我们限制了案例，我们假设没有索引$ n-1 $的把手。此外，我们现在仅考虑MOD 2系数。即将发表的论文将解决更一般的情况。作为一个应用程序，我们计算$ \ mathbb {cp}^2 $的自由循环空间的同源。
Let $Λ$ be a link of Legendrian spheres in the boundary of a subcritical $2n$-dimensional Weinstein manifold $X$. We show that, under some geometrical assumptions, the computation of the Legendrian contact homology of $Λ$ can be reduced to a computation of Legendrian contact homology in 1--jet spaces. Since the Legendrian contact homology in 1--jet spaces is well studied, this gives a simplified way to compute the Legendrian contact homology of $Λ$. We restrict to the case when the attaching spheres of the subcritical handles of $X$ do not interact with each other, and we assume that there are no handles of index $n-1$. Moreover, we will only consider mod 2 coefficients for now. The more general situation will be addressed in a forthcoming paper. As an application we compute the homology of the free loop space of $\mathbb{CP}^2$.
