Calabi quasimorphisms for the symplectic ball

Paul Biran, Michael Entov, Leonid Polterovich

Research output: Contribution to journalArticlepeer-review

50 Scopus citations

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.

Original languageEnglish
Pages (from-to)793-802
Number of pages10
JournalCommunications in Contemporary Mathematics
Volume6
Issue number5
DOIs
StatePublished - Oct 2004

Keywords

  • Hamiltonian diffeomorphism
  • Lagrangian submanifold
  • Quasimorphism
  • Symplectic manifold

ASJC Scopus subject areas

  • General Mathematics
  • Applied Mathematics

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