Nondensity results in high-dimensional stable Hamiltonian topology

Abstract

We push forward the study of higher dimensional stable Hamiltonian topology by establishing two nondensity results. First, we prove that stable hypersurfaces are not (Formula presented.) -dense in any isotopy class of embedded hypersurfaces on any ambient symplectic manifold of dimension (Formula presented.). Our second result is that on any manifold of dimension (Formula presented.), the set of non-degenerate stable Hamiltonian structures is not (Formula presented.) -dense among stable Hamiltonian structures in any given stable homotopy class that satisfies a mild assumption. The latter generalizes a result by Cieliebak and Volkov to arbitrary dimensions.