Refined Elementary Capacities from Symplectic Field Theory
Fuente:
arXiv
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2025
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866912541303635968 |
|---|---|
| author | Michala, Jonathan |
| author_facet | Michala, Jonathan |
| contents | We extend the family of capacities given by McDuff and Siegel by including a constraint $\ell$ on the number of positive asymptotically cylindrical ends of curves showing up in the definition. We prove a generalized computation formula for four-dimensional convex toric domains that offers new, sometimes sharp, embedding obstructions in stabilized and unstabilized cases. The formula restricts to the McDuff-Siegel capacities for $\ell = \infty$ and to the Gutt-Hutchings capacities for $\ell = 1$. To verify the formula, we must prove the existence of certain curves in the convex toric domain $X_Ω$, and this requires a new method of proof compared to McDuff-Siegel. We neck-stretch along $\partial X_Ω$ with curves known to exist in a well-chosen ellipsoid containing $X_Ω$, and we obtain the desired curves in the bottom level of the resulting psuedoholomorphic building. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_12525 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Refined Elementary Capacities from Symplectic Field Theory Michala, Jonathan Symplectic Geometry 53Dxx We extend the family of capacities given by McDuff and Siegel by including a constraint $\ell$ on the number of positive asymptotically cylindrical ends of curves showing up in the definition. We prove a generalized computation formula for four-dimensional convex toric domains that offers new, sometimes sharp, embedding obstructions in stabilized and unstabilized cases. The formula restricts to the McDuff-Siegel capacities for $\ell = \infty$ and to the Gutt-Hutchings capacities for $\ell = 1$. To verify the formula, we must prove the existence of certain curves in the convex toric domain $X_Ω$, and this requires a new method of proof compared to McDuff-Siegel. We neck-stretch along $\partial X_Ω$ with curves known to exist in a well-chosen ellipsoid containing $X_Ω$, and we obtain the desired curves in the bottom level of the resulting psuedoholomorphic building. |
| title | Refined Elementary Capacities from Symplectic Field Theory |
| topic | Symplectic Geometry 53Dxx |
| url | https://arxiv.org/abs/2508.12525 |