论文标题
在摩尔斯综合体上查看
The Poincaré-Lefschetz pairing viewed on Morse complexes
论文作者
论文摘要
鉴于具有非空边界的紧凑型歧管，并配备了通用的摩尔斯函数（也就是说，在边界上没有临界点，对边界的限制是摩尔斯的函数），我们已经知道如何构造两个摩尔斯群，一个产生绝对同源性，另一个产生相对同源性。在本说明中，我们构建了一个简短的精确序列，以及边界的莫尔斯复合物。此外，我们将相对摩尔斯复合物与绝对摩尔斯复合物的配对定义，该复合物以链链球链球链球菌的形式以同源性诱导相交产物。这是一种雄心勃勃的$ \ infty $ structures的雄心勃勃的方法的第一步。
Given a compact manifold with a non-empty boundary and equipped with a generic Morse function (that is, no critical point on the boundary and the restriction to the boundary is a Morse function), we already knew how to construct two Morse complexes, one yielding the absolute homology and the other the relative homology. In this note, we construct a short exact sequence from both of them and the Morse complex of the boundary. Moreover, we define a pairing of the relative Morse complex with the absolute Morse complex which induces the intersection product in homology, in the form due to S. Lefschetz. This the very first step in an ambitious approach towards A $\infty$-structures buildt from similar data.
