A characterization of heaviness in terms of relative symplectic cohomology

Abstract

For a compact subset K of a closed symplectic manifold (M, ω), 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.

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