论文标题
符合性摩尔斯理论和威特变形
Symplectic Morse Theory and Witten Deformation
论文作者
论文摘要
在符号歧管上，我们引入了一种摩尔斯式型复合物，其元素由摩尔斯函数的临界点对产生。复合物的差异由梯度流和梯度流线空间上的互合结构的整合。使用Witten变形方法，我们证明了该复合物的共同论与用于定义复合物的Riemannian指标和Morse函数无关，实际上是对Tsai，Tseng和Yau（TTY）差异形式的同构的同构。我们还获得了摩尔斯型不平等，这些不平等达到了TTY共同体的维度，并通过摩尔斯的临界点的数量以及符号结构与临界点的相互作用的相互作用。
On symplectic manifolds, we introduce a Morse-type complex with elements generated by pairs of critical points of a Morse function. The differential of the complex consists of gradient flows and an integration of the symplectic structure over spaces of gradient flow lines. Using the Witten deformation method, we prove that the cohomology of this complex is independent of both the Riemannian metric and the Morse function used to define the complex and is in fact isomorphic to the cohomology of differential forms of Tsai, Tseng and Yau (TTY). We also obtain Morse-type inequalities that bound the dimensions of the TTY cohomologies by the number of Morse critical points and the interaction of symplectic structure with the critical points.
