"Comuting symplectomorphisms and flux homomorphism"
Kawasaki, MorimichiLet $(S,\omega)$ be a closed connected oriented surface whose genus at least two equipped with a symplectic form. Then we show the ``non-extendability'' of Py's Calabi quasi-morphism, which is defined on the group of Hamiltonian diffeomorphisms. As its application, we obtain the vanishing of the cup product of the fluxes of commuting symplectomorphisms. This result may be regarded as an obstruction for commuting symplectomorphisms.