Quasi-morphismes et invariant de Calabi

Details Quasi-morphismes et invariant de Calabi Quasi-morphismes et invariant de Calabi

2005-06-06

arxiv.org/abs/math/0506096v2

Annales Scientifiques de l'Ecole normale sup\'erieure 39, no.1 (2006) 177--195

Mathematics

Symplectic Geometry

19 pages, juin 2005

Scientific paper

10.1016/j.ansens.2005.11.003

In this paper, we give two elementary constructions of homogeneous quasi-morphisms defined on the group of Hamiltonian diffeomorphisms of certain closed connected symplectic manifolds (or on its universal cover). The first quasi-morphism, 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 quasi-morphism 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.

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