PreprintCC BY 4.0arXiv
Obstructions in Symplectic Embedding Problems for Four-Dimensional Convex Toric Domains
Abstract
In Beyond ECH Capacities, Hutchings used the ECH cobordism map to produce obstructions for embedding one convex toric domain into another. We generalize the methods there to obstruct symplectic embeddings of a disjoint union of convex toric domains into another convex toric domain. We also find additional obstructions coming from intersection positivity and use similar methods to obstruct the existence of isotopies between two given symplectic embeddings.
Related
- Obstructions to embedding singular curves in toric varieties
- Strict lifts and cohomological obstructions in symplectic Lie--Rinehart--Jacobi prequantization
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BibTeX
@misc{coyne2026obstructions,
title = {{Obstructions in Symplectic Embedding Problems for Four-Dimensional Convex Toric Domains}},
author = {Theodore Coyne},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.07530},
eprint = {2610.07530},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.07530},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Obstructions in Symplectic Embedding Problems for Four-Dimensional Convex Toric Domains
AU - Theodore Coyne
PY - 2026
DA - 2026/10/05
PB - arXiv
DO - 10.48550/arxiv.2610.07530
UR - https://arxiv.org/abs/2610.07530
AB - In Beyond ECH Capacities, Hutchings used the ECH cobordism map to produce obstructions for embedding one convex toric domain into another. We generalize the methods there to obstruct symplectic embeddings of a disjoint union of convex toric domains into another convex toric domain. We also find additional obstructions coming from intersection positivity and use similar methods to obstruct the existence of isotopies between two given symplectic embeddings.
ER -