Hamiltonian unlinked subsets of a symplectic ball satisfy the spectral capacity packing inequality c(K1) + c(K2) <= a, and violating that inequality forces Hamiltonian linking.
On the spectral capacity of submanifolds
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abstract
The infimum of the spectral capacities of neighbourhoods of a nowhere coisotropic submanifold is shown to be zero. In contrast, neighbourhoods of a closed Lagrangian submanifold, and of certain contact-type hypersurfaces, are shown to have uniformly positive spectral capacity. Along the way we prove a quantitative Lagrangian control estimate relating spectral invariants, boundary depth, and the minimal area of holomorphic disks. The Lagrangian control also provides novel obstructions to certain Lagrangian embeddings into a symplectic ball.
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Hamiltonian linking and Symplectic packing
Hamiltonian unlinked subsets of a symplectic ball satisfy the spectral capacity packing inequality c(K1) + c(K2) <= a, and violating that inequality forces Hamiltonian linking.