# Ĝ-invariant quasimorphisms and symplectic geometry of surfaces

@article{Kawasaki2021invariantQA, title={Ĝ-invariant quasimorphisms and symplectic geometry of surfaces}, author={Morimichi Kawasaki and Mitsuaki Kimura}, journal={Israel Journal of Mathematics}, year={2021} }

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…

## 6 Citations

The space of non-extendable quasimorphisms

- Mathematics
- 2021

In the present paper, for a pair (G,N) of a group G and its normal subgroup N , we consider the space of quasimorphisms and quasi-cocycles on N non-extendable to G. To treat this space, we establish…

Extensions of quasi-morphisms to the symplectomorphism group of the disk

- MathematicsTopology and its Applications
- 2021

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-Ghys…

Bavard's duality theorem of invariant quasimorphisms

- Mathematics
- 2020

Let $H$ be a normal subgroup of a group $G$. A quasimorphism $f$ on $H$ is $G$-invariant if there is a non-negative number $D$ satisfying $|f(gxg^{-1}) - f(x)| \le D$ for every $g \in G$ and every $x…

Aut-invariant quasimorphisms on free products

- MathematicsAnnales mathématiques du Québec
- 2021

Let $$G=A *B$$
G
=
A
∗
B
be a free product of freely indecomposable groups. We explicitly construct quasimorphisms on G which are invariant with respect to all automorphisms of G. We also…

Aut-invariant quasimorphisms on graph products of abelian groups

- Mathematics
- 2021

The present paper constructs unbounded quasimorphisms that are invariant under all automorphisms on free products of more than two factors and on graph products of finitely generated abelian groups.…

Commuting symplectomorphisms on a surface and the flux homomorphism.

- Mathematics
- 2021

Let $(S,\omega)$ be a closed orientable surface whose genus $l$ is at least two. Then we provide an obstruction for commuting symplectomorphisms in terms of the flux homomorphism. More precisely, we…

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