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Computational analysis reveals stronger embedding obstructions in 4D symplectic ellipsoids' shape invariants, suggesting new insights for geometric topology.
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 obtained by considering only monotone tori.
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Hind et al. (2026) studied this question.
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