Heavy sets and index bounded relative symplectic cohomology (Q6566220)

Given a closed symplectic manifold \(M\) and a closed subset \(K\), one can use quantum cohomology and spectral invariants to define heavy and superheavy sets. Heavy sets are non-displaceable from itself and superheavy sets are non-displaceable from all heavy sets. On the other hand, one can define SH-heaviness and SH-superheaviness using the theory of relative symplectic cohomology by \textit{U. Varolgunes} [Geom. Topol. 25, No. 2, 547--642 (2021; Zbl 1475.53098)].\N\N\textit{A. Dickstein} et al. [``Symplectic topology and ideal-valued measures'', Preprint, \url{arXiv:2107.10012}] studied the relation between these notions and provided some sufficient conditions for a heavy set \(K\) to be SH-heavy. In the paper under review, the author studies the implication in the opposite direction and provides some sufficient conditions for a SH-heavy set \(K\) to be heavy.\N\NReaders are encouraged to look also at the follow-up work by \textit{C. Y. Mak} et al. [J. Topol. 17, No. 1, Article ID e12327, 26 p. (2024; Zbl 07824481)] for a recent progress on this problem.