Holomorphic planes in M× 𝕋^2 from weakly exact Lagrangians in M

Abstract

Let (M,ω_M) be closed symplectic manifold containing a closed Lagrangian submanifold L with ω_M vanishing on π₂(M,L). We prove that there is a nonconstant J-holomorphic plane u:ℂ→ M× 𝕋² for any almost complex structure $ J$ on M× 𝕋² tamed by ω_M⊕ω_std.

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BibTeX RIS

BibTeX

@misc{fuchs2026holomorphic,
  title = {{Holomorphic planes in $M\times \mathbbT^2$ from weakly exact Lagrangians in $M$}},
  author = {Urs Fuchs and Yuchen Yang},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2611.07799},
  eprint = {2611.07799},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2611.07799},
}

RIS

TY  - UNPB
TI  - Holomorphic planes in M× 𝕋^2 from weakly exact Lagrangians in M
AU  - Urs Fuchs
AU  - Yuchen Yang
PY  - 2026
DA  - 2026/11/05
PB  - arXiv
DO  - 10.48550/arxiv.2611.07799
UR  - https://arxiv.org/abs/2611.07799
AB  - Let (M,ω_M) be closed symplectic manifold containing a closed Lagrangian submanifold L with ω_M vanishing on π_2(M,L). We prove that there is a nonconstant J-holomorphic plane u:ℂ→ M× 𝕋^2 for any almost complex structure $ J$ on M× 𝕋^2 tamed by ω_M⊕ω_std.
ER  -

Holomorphic planes in M× 𝕋² from weakly exact Lagrangians in M

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