Heavy sets and index bounded relative symplectic cohomology

TL;DR

This paper uses relative symplectic cohomology and index bounded contact forms to identify heavy sets, linking SH-heaviness and heaviness, and addressing a conjecture in symplectic geometry.

Contribution

It establishes a connection between SH-heaviness and heaviness using relative symplectic cohomology, advancing understanding in symplectically aspherical manifolds.

Findings

Heavy sets can be detected via relative symplectic cohomology.

The relation between SH-heaviness and heaviness is clarified.

Partially resolves a conjecture by Dickstein-Ganor-Polterovich-Zapolsky.

Abstract

We use relative symplectic cohomology to detect heavy sets, with the help of index bounded contact forms. This establishes a relation between two notions SH-heaviness and heaviness, which partly answers a conjecture of Dickstein-Ganor-Polterovich-Zapolsky in the symplectically aspherical setting.