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

Abstract

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.

arXiv comment38 pages;v2: introduction rewritten, section 3.6 concerning open manifolds added, several typos corrected

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Cited by in corpus (7)

• Towards a dynamical interpretation of Hamiltonian spectral invariants on surfaces
• Quasi-morphisms on contactomorphism groups and contact rigidity
• Quasi-morphisms and quasi-states in symplectic topology
• Descent and C^0-rigidity of spectral invariants on monotone symplectic manifolds
• New energy-capacity-type inequalities and uniqueness of continuous Hamiltonians
• Hamiltonian Floer homology for compact convex symplectic manifolds
• Disjoint superheavy subsets and fragmentation norms