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A note on the cardinality of Lagrangian packings
[Une note sur la cardinalité des empilements lagrangiens]
Joé Brendel1 orcid ; Jean-Philippe Chassé2 orcid ; Laurent Côté3 orcid
1ETH Zürich, Rämistrasse 101, 8096 Zurich, Switzerland
2CRM, Université de Montréal, C.P. 6128 Succ. Centre-Ville, Montréal, QC H3C 3J7, Canada
3Mathematical Institute of the University of Bonn, Endenicher Allee 60, D-53115 Bonn, Germany
Comptes Rendus. Mathématique, Volume 364 (2026), pp. 353-362

Given a symplectic manifold, can one pack uncountably many Lagrangian submanifolds in a given Hamiltonian isotopy class of this symplectic manifold? We address $C^\infty $ and $C^0$ versions of this question.

Étant donnée une variété symplectique, pouvons-nous empiler une quantité indénombrable de sous-variétés lagrangiennes dans une classe d’isotopie hamiltonienne donnée de cette variété symplectique ? Nous traitons des versions $C^\infty $ et $C^0$ de cette question.

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Révisé le :
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DOI : 10.5802/crmath.835
Classification : 53D12, 53D05
Keywords: Lagrangian submanifolds, packing problems, $C^0$ symplectic topology
Mots-clés : Sous-variétés lagrangiennes, problèmes d’empilement, topologie symplectique $C^0$

Joé Brendel  1   ; Jean-Philippe Chassé  2   ; Laurent Côté  3

1 ETH Zürich, Rämistrasse 101, 8096 Zurich, Switzerland
2 CRM, Université de Montréal, C.P. 6128 Succ. Centre-Ville, Montréal, QC H3C 3J7, Canada
3 Mathematical Institute of the University of Bonn, Endenicher Allee 60, D-53115 Bonn, Germany
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits
Joé Brendel; Jean-Philippe Chassé; Laurent Côté. A note on the cardinality of Lagrangian packings. Comptes Rendus. Mathématique, Volume 364 (2026), pp. 353-362. doi: 10.5802/crmath.835
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     author = {Jo\'e Brendel and Jean-Philippe Chass\'e and Laurent C\^ot\'e},
     title = {A note on the cardinality of {Lagrangian} packings},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {353--362},
     year = {2026},
     publisher = {Acad\'emie des sciences, Paris},
     volume = {364},
     doi = {10.5802/crmath.835},
     language = {en},
}
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[1] Marcelo S. Atallah; Jean-Philippe Chassé; Rémi Leclercq; Egor Shelukhin Weinstein exactness of nearby Lagrangians and related questions (2025) | arXiv | Zbl

[2] Joé Brendel Hamiltonian classification of toric fibres and symmetric probes, Algebr. Geom. Topol., Volume 25 (2025) no. 3, pp. 1839-1876 | DOI | Zbl | MR

[3] Joé Brendel; Joontae Kim Lagrangian split tori in S 2 ×S 2 and billiards, Sel. Math., New Ser., Volume 31 (2025), 68, 39 pages | MR | Zbl

[4] Lev Buhovsky Towards the C 0 flux conjecture, Algebr. Geom. Topol., Volume 14 (2015) no. 6, pp. 3493-3508 | DOI | Zbl | MR

[5] Lev Buhovsky; Vincent Humilière; Sobhan Seyfaddini The action spectrum and C 0 symplectic topology, Math. Ann., Volume 380 (2021) no. 1, pp. 293-316 | DOI | Zbl

[6] Yuri V. Chekanov Lagrangian intersections, symplectic energy, and areas of holomorphic curves, Duke Math. J., Volume 95 (1998) no. 1, pp. 213-226 | Zbl | MR

[7] Yuri V. Chekanov; Felix Schlenk Lagrangian product tori in symplectic manifolds, Comment. Math. Helv., Volume 91 (2016) no. 3, pp. 445-475 | DOI | Zbl | MR

[8] Yasha Eliashberg A theorem on the structure of wave fronts and its applications in symplectic topology, Funct. Anal. Appl., Volume 21 (1987) no. 3, pp. 227-232 | DOI | Zbl

[9] Martin Golubitsky; Victor Guillemin Stable mappings and their singularities, Graduate Texts in Mathematics, 14, Springer, 2012 | Zbl | MR

[10] Misha Gromov Partial differential relations, Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge, 9, Springer, 1986 | DOI | Zbl

[11] Başak Gürel Totally non-coisotropic displacement and its applications to Hamiltonian dynamics, Commun. Contemp. Math., Volume 10 (2008) no. 06, pp. 1103-1128 | Zbl | DOI | MR

[12] Morris W. Hirsch Differential topology, Graduate Texts in Mathematics, 33, Springer, 2012 | Zbl | MR

[13] Vincent Humilière; Rémi Leclercq; Sobhan Seyfaddini Coisotropic rigidity and C 0 -symplectic geometry, Duke Math. J., Volume 164 (2015) no. 4, pp. 767-799 | Zbl

[14] François Laudenbach; Jean-Claude Sikorav Hamiltonian disjunction and limits of Lagrangian submanifolds, Int. Math. Res. Not., Volume 1994 (1994) no. 4, pp. 161-168 | DOI | Zbl | MR

[15] Cedric Membrez; Emmanuel Opshtein C 0 -rigidity of Lagrangian submanifolds and punctured holomorphic disks in the cotangent bundle, Compos. Math., Volume 157 (2021) no. 11, pp. 2433-2493 | DOI | Zbl | MR

[16] Leonid Polterovich; Egor Shelukhin Lagrangian configurations and Hamiltonian maps, Compos. Math., Volume 159 (2023) no. 12, pp. 2483-2520 | DOI | Zbl | MR

[17] Sobhan Seyfaddini C 0 -limits of Hamiltonian paths and the Oh–Schwarz spectral invariants, Int. Math. Res. Not., Volume 2013 (2013) no. 21, pp. 4920-4960 | DOI | Zbl | MR

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