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<p>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.</p>

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The shape invariant of four-dimensional ellipsoids

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年2月18日

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  • Richard Hind,
  • Jun Zhang

摘要

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.