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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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