Calabi quasi-morphisms for some non-monotone symplectic manifolds

Abstract

In this work we construct Calabi quasi-morphisms on the universal cover $\widetilde{Ham}\left(M\right)$ of the group of Hamiltonian diffeomorphisms for some non-monotone symplectic manifolds. This complements a result by Entov and Polterovich which applies in the monotone case. Moreover, in contrast to their work, we show that these quasi-morphisms descend to non-trivial homomorphisms on the fundamental group of $Ham\left(M\right)$.