Symplectic reduction of quasi-morphisms and quasi-states

Abstract

We prove that quasi-morphisms and quasi-states on a closed integral 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.Comment: 20 pages; v2: added remarks and updated references, to appear in Journal of Symplectic Geometr