Department of Mathematics2024-12-2920241753-841610.1112/topo.123272-s2.0-85187162799https://doi.org/10.1112/topo.12327https://hdl.handle.net/20.500.14288/22775For a compact subset K$K$ of a closed symplectic manifold (M,omega)$(M, \omega)$, we prove that K$K$ is heavy if and only if its relative symplectic cohomology over the Novikov field is nonzero. 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 is also included.MathematicsJournal article1753-84241181406800001Q140906