TY - JOUR
T1 - On the existence of symplectic barriers
AU - Haim-Kislev, Pazit
AU - Hind, Richard
AU - Ostrover, Yaron
N1 - Publisher Copyright:
© The Author(s) 2024.
PY - 2024/9
Y1 - 2024/9
N2 - In this note we establish the existence of a new type of rigidity of symplectic embeddings coming from obligatory intersections with symplectic planes. In particular, 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.
AB - In this note we establish the existence of a new type of rigidity of symplectic embeddings coming from obligatory intersections with symplectic planes. In particular, 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.
UR - http://www.scopus.com/inward/record.url?scp=85197380880&partnerID=8YFLogxK
U2 - 10.1007/s00029-024-00958-y
DO - 10.1007/s00029-024-00958-y
M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???
AN - SCOPUS:85197380880
SN - 1022-1824
VL - 30
JO - Selecta Mathematica, New Series
JF - Selecta Mathematica, New Series
IS - 4
M1 - 65
ER -