Displacement of polydisks and Lagrangian Floer theory

Details Displacement of polydisks and Lagrangian Floer theory Displacement of polydisks and Lagrangian Floer theory

2011-04-21

arxiv.org/abs/1104.4267v1

Mathematics

Symplectic Geometry

28 pages

Scientific paper

There are two purposes of the present article. One is to correct an error in the proof of Theorem 6.1.25 in \cite{fooo:book}, from which Theorem J \cite{fooo:book} follows. In the course of doing so, we also obtain a new lower bound of the displacement energy of polydisks in general dimension. The results of the present article are motivated by the recent preprint of Hind \cite{hind} where the 4 dimensional case is studied. Our proof is different from Hind's even in the 4 dimensional case and provides stronger result, and relies on the study of torsion thresholds of Floer cohomology of Lagrangian torus fiber in simple toric manifolds associated to the polydisks.

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