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arXiv · 1906.08429

Quasimorphisms on surfaces and continuity in the Hofer norm

Michael Khanevsky
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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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Michael Khanevsky. 2019-06-20. Quasimorphisms on surfaces and continuity in the Hofer norm. https://arxiv.org/abs/1906.08429

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