2025/07/17 by Djordjević, Danijel, Uljarević, Igor, Zhang, Jun
#53D35 #53D40 #55U99 #Dynamical Systems (math.DS) #FOS: Mathematics #Symplectic Geometry (math.SG)
paper · doi:10.48550/arxiv.2507.13234
This paper presents a systematic quantitative study of contact rigidity phenomena based on the contact Hamiltonian Floer theory established by Merry-Uljarević. Our quantitative approach applies to arbitrary admissible contact Hamiltonian functions on the contact boundary M = ∂ W of a \rm weakly+-monotone symplectic manifold W. From a theoretical standpoint, we develop a comprehensive contact spectral invariant theory. As applications, the properties of these invariants enable us to establish several fundamental results: the contact big fiber theorem, sufficient conditions for orderability, and the existence results of translated points. Furthermore, we uncover a non-traditional filtration structure on contact Hamiltonian Floer groups, which we formalize through the introduction of a novel type of persistence modules, called gapped modules, that are only parametrized by a partially ordered set. Among the various properties of contact spectral invariants, we highlight that the triangle inequality is derived through an innovative analysis of a pair-of-pants construction in the contact-geometric framework.