TY - JOUR
T1 - Packing Lagrangian tori
AU - Hind, Richard
AU - Kerman, Ely
N1 - Publisher Copyright:
© 2024 MSP (Mathematical Sciences Publishers).
PY - 2024
Y1 - 2024
N2 - We consider the problem of packing a symplectic manifold with integral Lagrangian tori, that is, Lagrangian tori whose area homomorphisms take only integer values. We prove that the Clifford torus in S2 × S2 is a maximal integral packing, in the sense that any other integral Lagrangian torus must intersect it. In the other direction, we show that in any symplectic polydisk P.a; b/ with a; b > 2, there is at least one integral Lagrangian torus in the complement of the collection of standard product integral Lagrangian tori. 53D12, 53D35.
AB - We consider the problem of packing a symplectic manifold with integral Lagrangian tori, that is, Lagrangian tori whose area homomorphisms take only integer values. We prove that the Clifford torus in S2 × S2 is a maximal integral packing, in the sense that any other integral Lagrangian torus must intersect it. In the other direction, we show that in any symplectic polydisk P.a; b/ with a; b > 2, there is at least one integral Lagrangian torus in the complement of the collection of standard product integral Lagrangian tori. 53D12, 53D35.
KW - Lagrangian intersections
KW - symplectic manifolds
UR - http://www.scopus.com/inward/record.url?scp=85203048827&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85203048827&partnerID=8YFLogxK
U2 - 10.2140/gt.2024.28.2207
DO - 10.2140/gt.2024.28.2207
M3 - Article
AN - SCOPUS:85203048827
SN - 1465-3060
VL - 28
SP - 2207
EP - 2257
JO - Geometry and Topology
JF - Geometry and Topology
IS - 5
ER -