For a compact subset of a closed symplectic manifold , we prove that 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.

中文翻译：

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用相对辛上同调描述重度

对于紧凑子集闭辛流形的，我们证明当且仅当其在诺维科夫场上的相对辛上同调非零时才是重的。作为一个应用，我们证明如果两个紧集不重且泊松通勤，那么它们的并集也不重。还包括对超重的讨论以及一些部分结果。