Packing Lagrangian tori

Hind, Richard; Kerman, Ely

doi:10.2140/gt.2024.28.2207

Download this article
	For screen
	For printing

Recent Issues

The Journal

Submission Guidelines

Submission Page

Policies for Authors

Ethics Statement

ISSN 1364-0380 (online)

ISSN 1465-3060 (print)

Author Index

To Appear

Other MSP Journals

Packing Lagrangian tori

Richard Hind and Ely Kerman

Geometry & Topology 28 (2024) 2207–2257

DOI: 10.2140/gt.2024.28.2207

Abstract

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.

Keywords

symplectic manifolds, Lagrangian intersections

Mathematical Subject Classification

Primary: 53D12, 53D35

References

Publication

Received: 15 February 2022

Revised: 27 October 2022

Accepted: 3 December 2022

Published: 24 August 2024

Proposed: Leonid Polterovich

Seconded: Dmitri Burago, Yakov Eliashberg

Authors

Richard Hind
Department of Mathematics University of Notre Dame Notre Dame, IN United States

Ely Kerman
Department of Mathematics University of Illinois at Urbana-Champaign Urbana, IL United States

Open Access made possible by participating institutions via Subscribe to Open.

Volume 28, issue 5 (2024)