In this work we construct Calabi quasi-morphisms on the universal cover 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 .
"Calabi quasi-morphisms for some non-monotone symplectic manifolds." Algebr. Geom. Topol. 6 (1) 405 - 434, 2006. https://doi.org/10.2140/agt.2006.6.405