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 ‐dense in any isotopy class of embedded hypersurfaces on any ambient symplectic manifold of dimension . Our second result is that on any manifold of dimension , the set of non‐degenerate stable Hamiltonian structures is not ‐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.