# Ĝ-invariant quasimorphisms and symplectic geometry of surfaces

@article{Kawasaki2021invariantQA,
title={Ĝ-invariant quasimorphisms and symplectic geometry of surfaces},
author={Morimichi Kawasaki and Mitsuaki Kimura},
journal={Israel Journal of Mathematics},
year={2021}
}
• Published 25 November 2019
• Mathematics
• Israel Journal of Mathematics
Let $\hat{G}$ be a group and $G$ its normal subgroup. In this paper, we study $\hat{G}$-invariant quasimorphisms on $G$ which appear in symplectic geometry and low dimensional topology. As its application, we prove the non-existence of a section of the flux homomorphism on closed surfaces of higher genus. We also prove that Py's Calabi quasimorphism and Entov-Polterovich's partial Calabi quasimorphism are non-extendable to the group of symplectomorphisms. We show that Py's Calabi quasimorphism…
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