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arXiv · 2201.09216

Strong closing property of contact forms and action selecting functors

Kei Irie
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Abstract

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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Kei Irie. 2022-01-23. Strong closing property of contact forms and action selecting functors. https://arxiv.org/abs/2201.09216

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