Elementary SFT Spectral Gaps And The Strong Closing Property

Abstract

We formulate elementary SFT spectral invariants of a large class of symplectic cobordisms and stable Hamiltonian manifolds, in any dimension. We give criteria for the strong closing property using these invariants, and verify these criteria for Hofer near periodic systems. This extends the class of symplectic dynamical systems in any dimension that satisfy the strong closing property.