# '22

36th Summer Topology Conference

July 18-22, 2022

University of Vienna, Department of Mathematics
Oskar-Morgenstern-Platz 1, 1090 Vienna, AUSTRIA

### "Comuting symplectomorphisms and flux homomorphism"

#### Kawasaki, Morimichi

Let $(S,\omega)$ 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.

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