Symplectic reduction of quasi-morphisms and quasi-states

We prove that quasi-morphisms and quasi-states on a closed rational symplectic manifold descend under symplectic reduction to symplectic hyperplane sections. Along the way we show that quasi-morphisms that arise from spectral invariants are the Calabi homomorphism when restricted to Hamiltonians supported on stably displaceable sets.

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Published 18 May 2012