Symplectic quasi-states on the quadric surface and Lagrangian submanifolds - Mathematics > Symplectic GeometryReport as inadecuate




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



Author: Yakov Eliashberg, Leonid Polterovich

Source: https://arxiv.org/







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