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arXiv · 2301.12625

A characterization of heaviness in terms of relative symplectic cohomology

Cheuk Yu Mak·Yuhan Sun·Umut Varolgunes
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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.

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Cheuk Yu Mak, Yuhan Sun, Umut Varolgunes. 2023-01-30. A characterization of heaviness in terms of relative symplectic cohomology. https://doi.org/10.1112/topo.12327

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