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We use relative symplectic cohomology to detect heavy sets, with the help ofindex bounded contact forms. The main result is a criterion for heaviness byusing the Viterbo restriction map, which establishes a relation betweenSH-heaviness and heaviness. This partly answers a conjecture ofDickstein-Ganor-Polterovich-Zapolsky in the current setting. Along the proof wealso construct spectral invariants of the relative symplectic cohomology forindex bounded Liouville domains.

Heavy sets and index bounded relative symplectic cohomology