Quasi-morphisms and symplectic quasi-states for convex symplectic manifolds

Details Quasi-morphisms and symplectic quasi-states for convex symplectic manifolds Quasi-morphisms and symplectic quasi-states for convex symplectic manifolds

2011-10-07

arxiv.org/abs/1110.1555v2

Mathematics

Symplectic Geometry

38 pages;v2: introduction rewritten, section 3.6 concerning open manifolds added, several typos corrected

Scientific paper

We use quantum and Floer homology to construct (partial) quasi-morphisms on the universal cover of the group of compactly supported Hamiltonian diffeomorphisms for a certain class of non-closed strongly semi-positive symplectic manifolds $(M,\omega)$. This leads to construction of (partial) symplectic quasi-states on the space 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.

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