On the Existence of Symplectic Barriers
Symplectic Geometry
2025-10-10 v2 Differential Geometry
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.
Keywords
Cite
@article{arxiv.2301.01822,
title = {On the Existence of Symplectic Barriers},
author = {Pazit Haim-Kislev and Richard Hind and Yaron Ostrover},
journal= {arXiv preprint arXiv:2301.01822},
year = {2025}
}