Symplectic quasi-states on the quadric surface and Lagrangian submanifolds

Abstract

The quantum homology of the monotone complex quadric surface splits into the sum of two fields. We outline a proof of the following statement: The unities of these fields give rise to distinct symplectic quasi-states defined by asymptotic spectral invariants. In fact, these quasi-states turn out to be "supported" on disjoint Lagrangian submanifolds. Our method involves a spectral sequence which starts at homology of the loop space of the 2-sphere and whose higher differentials are computed via symplectic field theory, in particular with the help of the Bourgeois-Oancea exact sequence.

arXiv comment22 pages

References in corpus (8)

• Compactness results in Symplectic Field Theory
• Rigid subsets of symplectic manifolds
• Geometry of contact transformations and domains: orderability versus squeezing
• Rigidity and uniruling for Lagrangian submanifolds
• Floer homology and the heat flow
• An exact sequence for contact- and symplectic homology
• Effect of Legendrian Surgery
• Toric degeneration and non-displaceable Lagrangian tori in $S^2\times S^2$

Cited by in corpus (8)

• Quasi-states, quasi-morphisms, and the moment map
• Symplectic Homology of complements of smooth divisors
• Quasi-morphisms and quasi-states in symplectic topology
• Faithful Semitoric Systems
• The affine invariant of generalized semitoric systems
• Classifying Toric and Semitoric Fans by Lifting Equations from ${\mathrm{SL}}_2(\mathbb{Z})$
• Symplectic theory of completely integrable Hamiltonian systems
• On exotic monotone Lagrangian tori in $\mathbb{C}{P}^2$ and $S^2\times S^2$