Symplectic quasi-states on the quadric surface and Lagrangian submanifolds

Details Symplectic quasi-states on the quadric surface and Lagrangian submanifolds Symplectic quasi-states on the quadric surface and Lagrangian submanifolds

2010-06-12

arxiv.org/abs/1006.2501v1

Mathematics

Symplectic Geometry

22 pages

Scientific paper

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.

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