切触形式的强封闭性与作用选择函子
Strong closing property of contact forms and action selecting functors
AI总结：
受三维Reeb流$C^\infty$封闭引理启发，研究提出切触形式的强封闭性概念，通过幺半函子构建其充分判据，并提出辛椭球边界标准切触形式满足该性质的猜想，为切触拓扑研究提供新方向。
摘要：
受三维Reeb流的$C^\infty$封闭引理启发，我们提出了切触形式的强封闭性概念。随后我们证明了强封闭性的一个充分判据，该判据通过考虑从带切触形式的流形范畴到滤过向量空间范畴的幺半函子来构建。作为该判据的一个潜在应用，我们提出了一个猜想：任意辛椭球边界上的标准切触形式都满足强封闭性。
英文摘要：
We introduce a notion of strong closing property of contact forms, inspired by the $C^\infty$ closing lemma for Reeb flows in dimension three. We then prove a sufficient criterion for strong closing property, which is formulated by considering a monoidal functor from a category of manifolds with contact forms to a category of filtered vector spaces. As a potential application of this criterion, we propose a conjecture which says that a standard contact form on the boundary of any symplectic ellipsoid satisfies strong closing property.
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