\hat{G}-invariant quasimorphisms and symplectic geometry of surfaces
\hat{G}-invariant quasimorphisms and symplectic geometry of surfaces
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hat{G}-不变拟同构和曲面的辛几何
DOI：
10.1007/s11856-021-2283-1
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发表时间：
2021
影响因子：
1
通讯作者：
Kimura Mitsuaki
中科院分区：
文献类型：
--
作者：
Kawasaki Morimichi;Kimura Mitsuaki
本文对群Ĝ及其正规子群G，研究了出现在辛几何和低维拓扑中的G上的Ĝ不变拟态。我们将证明Ĝ不变拟态射的Bavard型对偶和交换子长度的变体，并得到一些关于该长度的比较结果。作为应用，我们证明了高次范数闭曲面上的一段流量同态是不存在的，并证明了Py的Calabi拟态和Entov-Polterovich的部分Calabi拟态对于辛同态群是不可扩张的。
In this paper, for a groupĜand its normal subgroupG, we studyĜ-invariant quasimorphisms onGwhich appear in symplectic geometry and low dimensional topology. We will show a Bavard-type duality forĜ-invariant quasimorphisms and a variant of commutator length and obtain some comparison result on that length. As their 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 symplec-tomorphisms.