Quasimorphisms on surfaces and continuity in the Hofer norm
Symplectic Geometry
2019-06-21 v1
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.
Cite
@article{arxiv.1906.08429,
title = {Quasimorphisms on surfaces and continuity in the Hofer norm},
author = {Michael Khanevsky},
journal= {arXiv preprint arXiv:1906.08429},
year = {2019}
}