Packing Lagrangian tori

Hind, Richard¹ ; Kerman, Ely²

¹ Department of Mathematics, University of Notre Dame, Notre Dame, IN, United States
² Department of Mathematics, University of Illinois at Urbana-Champaign, Urbana, IL, United States

Geometry & topology, Tome 28 (2024) no. 5, pp. 2207-2257.

Résumé

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 $S^2\times S^2$ 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.

Détail

DOI : 10.2140/gt.2024.28.2207

Keywords: symplectic manifolds, Lagrangian intersections

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