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PreprintarXiv licencearXiv

Constructing Lagrangian surfaces in all symplectic toric $4$-manifolds from multi-grid diagrams

  • Shintaro Fushida-Hardy
  • Laura Wakelin
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Abstract

We present a new diagrammatic construction of Lagrangian surfaces in all symplectic toric $4$-manifolds from objects called multi-grid diagrams. These are a generalisation of triple grid diagrams for Lagrangian surfaces in ℂℙ2 wherein the underlying trisection is replaced by the more general notion of a toric decomposition. We give examples of multi-grid diagrams for Lagrangian surfaces in a range of symplectic toric $4$-manifolds, including Evans' recent non-squeezable Klein bottle in S2 × S2.

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Cite

BibTeXRIS
BibTeX
@misc{fushidahardy2026constructing,
  title = {{Constructing Lagrangian surfaces in all symplectic toric $4$-manifolds from multi-grid diagrams}},
  author = {Shintaro Fushida-Hardy and Laura Wakelin},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.42076},
  eprint = {2610.42076},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.42076},
}
RIS
TY  - UNPB
TI  - Constructing Lagrangian surfaces in all symplectic toric $4$-manifolds from multi-grid diagrams
AU  - Shintaro Fushida-Hardy
AU  - Laura Wakelin
PY  - 2026
DA  - 2026/10/30
PB  - arXiv
DO  - 10.48550/arxiv.2610.42076
UR  - https://arxiv.org/abs/2610.42076
AB  - We present a new diagrammatic construction of Lagrangian surfaces in all symplectic toric $4$-manifolds from objects called multi-grid diagrams. These are a generalisation of triple grid diagrams for Lagrangian surfaces in ℂℙ^2 wherein the underlying trisection is replaced by the more general notion of a toric decomposition. We give examples of multi-grid diagrams for Lagrangian surfaces in a range of symplectic toric $4$-manifolds, including Evans' recent non-squeezable Klein bottle in S^2 × S^2.
ER  -