闭1-形式的零点计数
Counting zeros of closed 1-forms
摘要：
本文给出了闭1-型在给定上同调类内零点个数的新的拓扑下界。主要的新技术工具是变形复合体，它允许传递到奇异极限，并将具有封闭1-形式的原始问题简化为具有Morse函数的传统问题。我们通过例子表明，建议的方法可以提供更强的估计比Novikov不等式。在Bott非退化假设下，本文的方法也适用于研究闭1-形式零点集的拓扑。
英文摘要：
The paper suggests new topological lower bounds for the number of zeros of closed 1-forms within a given cohomology class. The main new technical tool is the deformation complex, which allows to pass to a singular limit and reduce the original problem with a closed 1-form to a traditional problem with a Morse function. We show by examples that the suggested approach may provide stronger estimates than the Novikov inequalities. The technique of the paper also applies to study topology of the set of zeros of closed 1-forms under Bott non-degeneracy assumptions.
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