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arXiv · 1911.10855

$\hat{G}$-invariant quasimorphisms and symplectic geometry of surfaces

Morimichi Kawasaki·Mitsuaki Kimura
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Abstract

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 is the unique non-extendable quasimorphism to some group.

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Morimichi Kawasaki, Mitsuaki Kimura. 2019-11-25. $\hat{G}$-invariant quasimorphisms and symplectic geometry of surfaces. https://arxiv.org/abs/1911.10855

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