The shape invariant of symplectic ellipsoids
arXiv:2010.02185
Abstract
The shape invariant of a symplectic manifold encodes the possible area classes of embedded Lagrangian tori. Potentially this is a powerful invariant, but for most manifolds the shape is unknown. We compute the shape for 4 dimensional symplectic ellipsoids where the ratio of the factors is an integer. The full shape invariant gives stronger embedding obstructions than results by considering only monotone tori.
minor changes; references updated; a new section on the Hamiltonian shape invariant added