A characterization of heaviness in terms of relative symplectic cohomology

Abstract

For a compact subset $K$ of a closed symplectic manifold $(M,\omega )$, we prove that $K$ is heavy if and only if its relative symplectic cohomology over the Novikov field is non-zero. As an application we show that if two compact sets are not heavy and Poisson commuting, then their union is also not heavy. A discussion on superheaviness together with some partial results are also included.

Added Corollary 1.10. To appear in the Journal of Topology

References in corpus (1)

• Mayer-Vietoris property for relative symplectic cohomology