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

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.

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)

References in corpus (1)

• Quasi-morphisms and quasi-states in symplectic topology