Journal of Symplectic Geometry

Volume 19 (2021)

Number 5

Non-degeneracy of the Hofer norm for Poisson structures

Pages: 1095 – 1100

DOI: https://dx.doi.org/10.4310/JSG.2021.v19.n5.a3

Authors

Dušan Joksimović (Institut de Mathématiques de Jussieu, Paris Rive Gauche, Paris, France)

Ioan Mărcuţ (IMAPP, Radboud University Nijmegen, Netherlands)

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 follows from the symplectic case after reducing the problem to a symplectic leaf.

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Received 3 August 2020

Accepted 19 October 2020

Published 27 May 2022