Strong closing property of contact forms and action selecting functors

2022/01/23 by Irie, Kei · 2 citations
#53D42 #70H12 #Dynamical Systems (math.DS) #FOS: Mathematics #Symplectic Geometry (math.SG)

paper · doi:10.48550/arxiv.2201.09216

Abstract

We introduce a notion of strong closing property of contact forms, inspired by the C^∞ 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.

Cited by

• Strong closing lemmas in Hamiltonian dynamics
• Orbifold Floer spectral invariants, symmetric product links and Weyl laws

Related

• Contact homology and higher dimensional closing lemmas
• Strong closing lemmas in Hamiltonian dynamics
• Constructions of contact forms on products and piecewise fibered\n manifolds
• Reeb flows with small contact volume and large return time to a global\n section
• Contact forms with large systolic ratio in arbitrary dimensions