A max inequality for spectral invariants of disjointly supported Hamiltonians

We study the relation between spectral invariants of disjointly supported Hamiltonians and of their sum. On aspherical manifolds, such a relation was established by Humilière, 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.

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Received 21 May 2021

Accepted 15 January 2022

Published 24 April 2023