English

The shape invariant of symplectic ellipsoids

Symplectic Geometry 2021-02-10 v2

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.

Keywords

Cite

@article{arxiv.2010.02185,
  title  = {The shape invariant of symplectic ellipsoids},
  author = {Richard Hind and Jun Zhang},
  journal= {arXiv preprint arXiv:2010.02185},
  year   = {2021}
}

Comments

minor changes; references updated; a new section on the Hamiltonian shape invariant added