Ĝ-invariant quasimorphisms and symplectic geometry of surfaces

  title={Ĝ-invariant quasimorphisms and symplectic geometry of surfaces},
  author={Morimichi Kawasaki and Mitsuaki Kimura},
  journal={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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