Unknottedness of real Lagrangian tori in $S^2\times S^2$

Joontae Kim

Unknottedness of real Lagrangian tori in $S^2\times S^2$

Symplectic Geometry 2020-07-14 v2 Geometric Topology

Authors: Joontae Kim

Abstract

We prove the Hamiltonian unknottedness of real Lagrangian tori in the monotone $S^2\times S^2$ , namely any real Lagrangian torus in $S^2\times S^2$ is Hamiltonian isotopic to the Clifford torus $\mathbb{T}_{\text{Clif}}$ . The proof is based on a neck-stretching argument, Gromov's foliation theorem, and the Cieliebak-Schwingenheuer criterion.

Keywords

lagrangian torus hamiltonian unknottedness clifford torus neck-stretching symplectic geometry

Cite

@article{arxiv.2003.04528,
  title  = {Unknottedness of real Lagrangian tori in $S^2\times S^2$},
  author = {Joontae Kim},
  journal= {arXiv preprint arXiv:2003.04528},
  year   = {2020}
}

Comments

16 pages, various improvements, to appear in Math. Ann

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