论文标题
本地摩尔斯摩尔斯的相对杯状长度
The relative cup-length in local Morse cohomology
论文作者
论文摘要
当地的摩尔斯摩尔斯共同体学使共同体学团体隔离了摩尔斯的梯度流的邻域（通常是非压缩）riemannian流形$ m $。我们表明，局部摩尔斯的共同体是隔离社区共同体的一个模块，这使我们能够定义相对于隔离邻居的共同体的杯状长度，该杯子对不一定是Morse的$ M $的关键功能点的临界点数量下降。最后，我们以一个例子说明，这种下限确实可以比绝对杯长度给出的下限要强。
Local Morse cohomology associates cohomology groups to isolating neighborhoods of gradient flows of Morse functions on (generally non-compact) Riemannian manifolds $M$. We show that local Morse cohomology is a module over the cohomology of the isolating neighborhood, which allows us to define a cup-length relative to the cohomology of the isolating neighborhood that gives a lower bound on the number of critical points of functions on $M$ that are not necessarily Morse. Finally, we illustrate by an example that this lower bound can indeed be stronger than the lower bound given by the absolute cup-length.
