Quasimorphisms on surfaces and continuity in the Hofer norm

2019/06/20 by Khanevsky, Michael · 1 citation
#FOS: Mathematics #Symplectic Geometry (math.SG)

paper · doi:10.48550/arxiv.1906.08429

Abstract

There is a number of known constructions of quasimorphisms on Hamiltonian groups. We show that on surfaces many of these quasimorphisms are not compatible with the Hofer norm in a sense they are not continuous and not Lipschitz. The only exception known to the author is the Calabi quasimorphism on a sphere and the induced quasimorphisms on genus-zero surfaces.

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• Balanced curves, quasimorphisms, and the equator conjecture

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