A max inequality for spectral invariants of disjointly supported Hamiltonians

TL;DR

This paper investigates how spectral invariants of disjoint Hamiltonians relate to their sum, extending known results to broader contexts and applying findings to Poisson bracket invariants and superheavy sets.

Contribution

It generalizes a spectral invariant inequality from aspherical manifolds to more general settings, with implications for symplectic topology.

Findings

Established a weaker spectral invariant relation in wider settings.

Applied results to Poisson bracket invariants.

Connected spectral invariants to superheavy sets.

Abstract

We study the relation between spectral invariants of disjointly supported Hamiltonians and of their sum. On aspherical manifolds, such a relation was established by Humili\`ere, Le Roux and Seyfaddini. We show that a weaker statement holds in a wider setting, and derive applications to Polterovich's Poisson bracket invariant and to Entov and Polterovich's notion of superheavy sets.