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arXiv · 2301.01822

On the Existence of Symplectic Barriers

Pazit Haim-Kislev·Richard Hind·Yaron Ostrover
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Abstract

In this note we establish the existence of a new type of rigidity of symplectic embeddings coming from obligatory intersections with symplectic planes. More precisely, we prove that if a Euclidean ball is symplectically embedded in the Euclidean unit ball, then it must intersect a sufficiently fine grid of two-codimensional pairwise disjoint symplectic planes. Inspired by analogous terminology for Lagrangian submanifolds, we refer to these obstructions as symplectic barriers.

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Pazit Haim-Kislev, Richard Hind, Yaron Ostrover. 2023-01-04. On the Existence of Symplectic Barriers. https://doi.org/10.1007/s00029-024-00958-y

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