@article{3019dc0fdfc4489d8b970328f333eb63,
title = "Calabi quasimorphisms for the symplectic ball",
abstract = "We prove that the group of compactly supported symplectomorphisms of the standard symplectic ball admits a continuum of linearly independent real-valued homogeneous quasimorphisms. In addition these quasimorphisms are Lipschitz in the Hofer metric and have the following property: the value of each such quasimorphism on any symplectomorphism supported in any {"}sufficiently small{"} open subset of the ball equals the Calabi invariant of the symplectomorphism. By a {"}sufficiently small{"} open subset we mean that it can be displaced from itself by a symplectomorphism of the ball. As a byproduct we show that the (Lagrangian) Clifford torus in the complex projective space cannot be displaced from itself by a Hamiltonian isotopy.",
keywords = "Hamiltonian diffeomorphism, Lagrangian submanifold, Quasimorphism, Symplectic manifold",
author = "Paul Biran and Michael Entov and Leonid Polterovich",
note = "Funding Information: We thank Slava Kerner and Felix Schlenk who read a preliminary version of this paper and made a number of corrections. The second author is partially supported by the Fund for Promotion of Research at Technion and by the Israel Science Foundation grant # 68/02. The third author is supported by the Israel Science Foundation founded by the Israel Academy of Sciences and Humanities.",
year = "2004",
month = oct,
doi = "10.1142/S0219199704001525",
language = "אנגלית",
volume = "6",
pages = "793--802",
journal = "Communications in Contemporary Mathematics",
issn = "0219-1997",
publisher = "World Scientific",
number = "5",
}