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

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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 nondisplaceable 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.

Original languageEnglish (US)
Pages (from-to)2497-2533
Number of pages37
JournalInternational Mathematics Research Notices
Volume2013
Issue number11
DOIs
StatePublished - Jan 1 2013
Externally publishedYes

ASJC Scopus subject areas

  • Mathematics(all)

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