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We use quantum and Floer homology to construct (partial) quasi-morphisms on the universal coverof the group of compactly supported Hamiltonian diffeomorphisms for a certain class of nonclosed strongly semi-positive symplectic manifolds ( M , ω ). This leads to a construction of (partial) symplectic quasi-states on the space  C   cc  ( M ) of continuous functions on  M  that are constant near infinity. The work extends the results by Entov and Polterovich which apply in the closed case.

Quasi-morphisms and Symplectic Quasi-states for Convex Symplectic Manifolds