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Quasi-morphisms and symplectic quasi-states for convex symplectic manifolds. (English) Zbl 1329.53119
Summary: We use quantum and Floer homology to construct (partial) quasi-morphisms on the universal cover $$\widetilde{\mathrm{Ham}}(M,\omega)$$ of the group of compactly supported Hamiltonian diffeomorphisms for a certain class of nonclosed strongly semi-positive symplectic manifolds ($$M,\omega$$). 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.

##### MSC:
 53D40 Symplectic aspects of Floer homology and cohomology
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