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

Yuhan Sun (Department of Mathematics, Rutgers University, Piscataway, New Jersey, U.S.A.; and Department of Mathematics, Stony Brook University, Stony Brook, New York, U.S.A.)

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.

Full Text (PDF format)

Received 9 June 2020

Accepted 4 September 2022

Published 22 December 2023