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Journal of Symplectic Geometry
Volume 21 (2023)
Number 3
Displacement energy of Lagrangian $3$-spheres
Pages: 509 – 601
DOI: https://dx.doi.org/10.4310/JSG.2023.v21.n3.a3
Author
Abstract
We estimate the displacement energy of Lagrangian $3$-spheres in a symplectic $6$-manifold $X$, by estimating the displacement energy of a one-parameter family $L^\lambda$ of Lagrangian tori near the sphere. The proof establishes a new version of Lagrangian Floer theory with cylinder corrections, which is motivated by the change of open Gromov–Witten invariants under the conifold transition. We also make observations and computations on the classical Floer theory by using the symplectic sum formula and Welschinger invariants.
Received 9 June 2020
Accepted 4 September 2022
Published 22 December 2023