Quasi-states, quasi-morphisms, and the moment map

Details Quasi-states, quasi-morphisms, and the moment map Quasi-states, quasi-morphisms, and the moment map

2011-05-09

arxiv.org/abs/1105.1805v3

Mathematics

Symplectic Geometry

22 pages, 7 figures; v3: minor corrections, added remarks, and altered numbering scheme to match published version. To appear

Scientific paper

We prove that symplectic quasi-states and quasi-morphisms on a symplectic manifold descend under symplectic reduction on a superheavy level set of a Hamiltonian torus action. Using a construction due to Abreu and Macarini, in each dimension at least four we produce a closed symplectic toric manifold with infinite dimensional spaces of symplectic quasi-states and quasi-morphisms, and a one-parameter family of non-displaceable Lagrangian tori. By using McDuff's method of probes, we also show how Ostrover and Tyomkin's method for finding distinct spectral quasi-states in symplectic toric Fano manifolds can also be used to find different superheavy toric fibers.

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