$\hat{G}$-invariant quasimorphisms and symplectic geometry of surfaces
Abstract
Let be a group and its normal subgroup. In this paper, we study -invariant quasimorphisms on 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.
Keywords
Cite
@article{arxiv.1911.10855,
title = {$\hat{G}$-invariant quasimorphisms and symplectic geometry of surfaces},
author = {Morimichi Kawasaki and Mitsuaki Kimura},
journal= {arXiv preprint arXiv:1911.10855},
year = {2020}
}
Comments
We added new results on $C^0$-symplectic topology (Corollary 6.2 and Theorem 6.5) and the space of non-extendable quasimorphisms (Theorem 1.17 and Corollary1.18). We also prove that Py's Calabi quasimorphism is the "unique" non-extendable quasimorphism in some sense (Corollary 1.19)