Corpus ID: 208267972

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

@article{Kawasaki2019hatGinvariantQA,
title={\$\hat\{G\}\$-invariant quasimorphisms and symplectic geometry of surfaces},
author={Morimichi Kawasaki and Mitsuaki Kimura},
journal={arXiv: Symplectic Geometry},
year={2019}
}
• Published 25 November 2019
• Mathematics
• arXiv: Symplectic Geometry
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… Expand
2 Citations
Extensions of quasi-morphisms to the symplectomorphism group of the disk
On the group $\rm{Symp}(D, \partial D)$ of symplectomorphisms of the disk which are the identity near the boundary, there are homogeneous quasi-morphisms called the Ruelle invariant and Gambaudo-GhysExpand
Bavard's duality theorem of invariant quasimorphisms
• Mathematics
• 2020