Hamiltonian commutators with large Hofer norm

TL;DR

This paper demonstrates that commutators of Hamiltonian diffeomorphisms can have arbitrarily large Hofer norm, providing new insights into symplectic geometry and answering a question by McDuff and Polterovich.

Contribution

It introduces a technique to show large Hofer norms for commutators on surfaces of positive genus and their products, advancing understanding in symplectic topology.

Findings

Commutators of Hamiltonian diffeomorphisms can have arbitrarily large Hofer norm.

The technique applies to positive genus surfaces and their products.

Partial answer to McDuff and Polterovich's question.

Abstract

We show that commutators of Hamiltonian diffeomorphisms may have arbitrarily large Hofer norm. The proposed technique is applicable to positive genus surfaces and their products. This gives partial answer to a question by McDuff and Polterovich.