G-invariant quasimorphisms and symplectic geometry of surfaces

2019/11/25 by Kawasaki, Morimichi, Kimura, Mitsuaki
#FOS: Mathematics #Geometric Topology (math.GT) #Group Theory (math.GR) #Symplectic Geometry (math.SG)

paper · doi:10.48550/arxiv.1911.10855

Abstract

Let G be a group and G its normal subgroup. In this paper, we study 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.

Related

• Quasimorphisms on surfaces and continuity in the Hofer norm
• Calabi quasimorphisms for the symplectic ball
• Py-Calabi quasi-morphisms and quasi-states on orientable surfaces of higher genus
• Invariant quasimorphisms for groups acting on the circle and non-equivalence of SCL
• The Calabi invariant for some groups of homeomorphisms