Kirwan-Novikov inequalities on a manifold with boundary
Kirwan-Novikov inequalities on a manifold with boundary
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有边界流形上的 Kirwan-Novikov 不等式
DOI：
10.1090/s0002-9947-06-04021-9
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发表时间：
2004
影响因子：
1.3
通讯作者：
V. Silantyev
中科院分区：
文献类型：
--
作者：
M. Braverman;V. Silantyev
我们在两个方向上扩展闭 1-形式的诺维科夫莫尔斯型不等式。首先，我们考虑有边界的流形。其次，我们允许该形式的临界集具有非常退化的结构，仅假设该形式在 Kirwan 意义上是非退化的。特别是，我们获得了关于有边界流形上的常见莫尔斯不等式的 Floer 结果的推广。我们还获得了不等式的等变版本。我们的证明基于威滕变形技术的应用。这里的主要新颖之处在于我们将临界集的邻域视为具有圆柱形末端的流形。这使得局部分析大大简化。特别是，我们获得了闭流形上的 Morse-Bott 不等式的新解析证明。
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.