Quasimorphismes et invariant de Calabi
Abstract
In this paper, we give two elementary constructions of homogeneous quasimorphisms defined on the group of Hamiltonian diffeomorphisms of certain closed connected symplectic manifolds (or on its universal cover). The first quasimorphism, denoted by $\calabi\_{S}$, is defined on the group of Hamiltonian diffeomorphisms of a closed oriented surface $S$ of genus greater than 1. This construction is motivated by a question of M. Entov and L. Polterovich. If $U\subset S$ is a disk or an annulus, the restriction of $\calabi\_{S}$ to the subgroup of diffeomorphisms which are the time one map of a Hamiltonian isotopy in $U$ equals Calabi's homomorphism. The second quasimorphism is defined on the universal cover of the group of Hamiltonian diffeomorphisms of a symplectic manifold for which the cohomology class of the symplectic form is a multiple of the first Chern class.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 June 2005
 DOI:
 10.48550/arXiv.math/0506096
 arXiv:
 arXiv:math/0506096
 Bibcode:
 2005math......6096P
 Keywords:

 Mathematics  Symplectic Geometry;
 Mathematics  Group Theory;
 20J06;
 53D05
 EPrint:
 19 pages, juin 2005