On continuity of quasi-morphisms for symplectic maps
Dynamical Systems
2012-05-25 v1 Symplectic Geometry
Abstract
We discuss -continuous homogeneous quasi-morphisms on the identity component of the group of compactly supported symplectomorphisms of a symplectic manifold. Such quasi-morphisms extend to the -closure of this group inside the homeomorphism group. We show that for standard symplectic balls of any dimension, as well as for compact oriented surfaces, other than the sphere, the space of such quasi-morphisms is infinite-dimensional. In the case of surfaces, we give a user-friendly topological characterization of such quasi-morphisms. We also present an application to Hofer's geometry on the group of Hamiltonian diffeomorphisms of the ball.
Cite
@article{arxiv.0904.1397,
title = {On continuity of quasi-morphisms for symplectic maps},
author = {Michael Entov and Leonid Polterovich and Pierre Py},
journal= {arXiv preprint arXiv:0904.1397},
year = {2012}
}
Comments
with an appendix by Michael Khanevsky