On continuity of quasi-morphisms for symplectic maps
Entov, Michael ; Polterovich, Leonid ; Py, Pierre
arXiv, 0904.1397 / Harvested from arXiv
Text on arXiv
We discuss $C^0$-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 $C^0$-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.
Publié le : 2009-04-08
Classification:  Mathematics - Dynamical Systems,  Mathematics - Symplectic Geometry,  37E30, 57S05, 53D99 
@article{0904.1397,
     author = {Entov, Michael and Polterovich, Leonid and Py, Pierre},
     title = {On continuity of quasi-morphisms for symplectic maps},
     journal = {arXiv},
     volume = {2009},
     number = {0},
     year = {2009},
     language = {en},
     url = {http://dml.mathdoc.fr/item/0904.1397}
}

Entov, Michael; Polterovich, Leonid; Py, Pierre. On continuity of quasi-morphisms for symplectic maps. arXiv, Tome 2009 (2009) no. 0, . http://gdmltest.u-ga.fr/item/0904.1397/