标题： 边界流形上的Kirwan-Novikov不等式 显示英文标题

标题： Kirwan-Novikov inequalities on a manifold with boundary

摘要： 我们扩展了闭1-形式的诺维科夫莫尔斯型不等式，有两个方向。 首先，我们考虑带有边界的流形。 其次，我们允许该形式临界集非常退化的结构，仅假设该形式在基尔万的意义下是非退化的。 特别是，我们得到了弗洛尔关于带边界流形上通常莫尔斯不等式结果的一个推广。 我们还得到了不等式的一个等变版本。 我们的证明基于威滕变形技术的应用。 这里的最大创新是，我们将临界集的邻域视为一个具有圆柱端的流形。 这导致了局部分析的显著简化。 特别是，我们得到了闭流形上莫尔斯-博特不等式的新解析证明。 显示英文摘要

摘要： We extend the Novikov Morse-type inequalities for closed 1-forms in 2 directions. First, we consider manifolds with boundary. Second, we allow a very degenerate structure of the critical set of the form, assuming only that the form is non-degenerated in the sense of Kirwan. In particular, we obtain a generalization of a result of Floer about the usual Morse inequalities on a manifold with boundary. We also obtain an equivariant version of our inequalities. Our proof is based on an application of the Witten deformation technique. The main novelty here is that we consider the neighborhood of the critical set as a manifold with a cylindrical end. This leads to a considerable simplification of the local analysis. In particular, we obtain a new analytic proof of the Morse-Bott inequalities on a closed manifold.