2025/08/17 by Jonathan Michala, Michala, Jonathan
Chemistry · Physics and Astronomy · #53Dxx #Advanced Physical and Chemical Molecular Interactions #FOS: Mathematics #Quantum Mechanics and Non-Hermitian Physics #Quantum chaos and dynamical systems #Symplectic Geometry (math.SG)
paper · pdf · doi:10.48550/arxiv.2508.12525
openalex publication_date 2025/08/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We extend the family of capacities given by McDuff and Siegel by including a constraint ℓ 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 ℓ = ∞ and to the Gutt-Hutchings capacities for ℓ = 1. To verify the formula, we must prove the existence of certain curves in the convex toric domain XΩ, and this requires a new method of proof compared to McDuff-Siegel. We neck-stretch along ∂ XΩ with curves known to exist in a well-chosen ellipsoid containing XΩ, and we obtain the desired curves in the bottom level of the resulting psuedoholomorphic building.