Non-degeneracy of the Hofer norm for Poisson structures

TL;DR

This paper demonstrates that the Hofer norm on the Hamiltonian group of a Poisson manifold is non-degenerate, extending a key property from symplectic to Poisson geometry using symplectic topology tools.

Contribution

It proves the non-degeneracy of the Hofer norm for Poisson structures, a result previously known only in symplectic geometry.

Findings

Hofer norm is non-degenerate on Poisson manifolds

Uses symplectic topology tools for proof

Extends symplectic results to Poisson setting

Abstract

We remark that, as in the symplectic case, the Hofer norm on the Hamiltonian group of a Poisson manifold is non-degenerate. The proof is a straightforward application of tools from symplectic topology.