Quasi-states, quasi-morphisms, and the moment map
Abstract
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.
Keywords
Cite
@article{arxiv.1105.1805,
title = {Quasi-states, quasi-morphisms, and the moment map},
author = {Matthew Strom Borman},
journal= {arXiv preprint arXiv:1105.1805},
year = {2013}
}
Comments
22 pages, 7 figures; v3: minor corrections, added remarks, and altered numbering scheme to match published version. To appear in International Mathematics Research Notices