Calabi quasimorphisms for the symplectic ball

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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.
Minor errors corrected. To appear in Communications in Contemporary Mathematics

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Symplectic Geometry, Differential Geometry, 53D22, 53D05, 53D40, 53D45

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http://salesiana.dossiersoluciones.com/handle/123456789/67942

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0307011
 http://arxiv.org/abs/math/0307011

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arXiv