no. 4
Sheaf quantization and intersection of rational Lagrangian immersions
[Quantification faisceautique et intersection d’immersions lagrangiennes rationnelles]
Asano, Tomohiro1 ; Ike, Yuichi2
1 Graduate School of Mathematical Sciences, The University of Tokyo 3-8-1 Komaba, Meguro-ku, Tokyo (Japan)
2 Graduate School of Information Science and Technology, The University of Tokyo 7-3-1 Hongo, Bunkyo-ku, Tokyo (Japan)
Annales de l'Institut Fourier, Tome 73 (2023) no. 4, pp. 1533-1587.

Nous étudions les immersions lagrangiennes rationnelles dans un fibré cotangent en nous basant sur la théorie microlocale des faisceaux. Nous construisons une quantification faisceautique d’une immersion lagrangienne rationnelle et étudions ses propriétés dans la catégorie de Tamarkin. En utilisant la quantification faisceautique, nous donnons une limite explicite à l’énergie de déplacement et une estimation Betti ou cup-length pour le nombre de points d’intersection de l’immersion et de son image hamiltonienne par une méthode purement faisceautique.

We study rational Lagrangian immersions in a cotangent bundle, based on the microlocal theory of sheaves. We construct a sheaf quantization of a rational Lagrangian immersion and investigate its properties in Tamarkin category. Using the sheaf quantization, we give an explicit bound for the displacement energy and a Betti/cup-length estimate for the number of the intersection points of the immersion and its Hamiltonian image by a purely sheaf-theoretic method.

Reçu le :
Révisé le :
Accepté le :
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DOI : 10.5802/aif.3554
Classification : 53D12, 37J10, 53D35, 35A27
Keywords: Lagrangian immersions, displacement energy, microlocal theory of sheaves.
Mot clés : Immersions lagrangiennes, énergie de déplacement, théorie microlocale des faisceaux.
Asano, Tomohiro 1 ; Ike, Yuichi 2

1 Graduate School of Mathematical Sciences, The University of Tokyo 3-8-1 Komaba, Meguro-ku, Tokyo (Japan)
2 Graduate School of Information Science and Technology, The University of Tokyo 7-3-1 Hongo, Bunkyo-ku, Tokyo (Japan)
Licence : CC-BY-ND 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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     title = {Sheaf quantization and intersection of rational {Lagrangian} immersions},
     journal = {Annales de l'Institut Fourier},
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Asano, Tomohiro; Ike, Yuichi. Sheaf quantization and intersection of rational Lagrangian immersions. Annales de l'Institut Fourier, Tome 73 (2023) no. 4, pp. 1533-1587. doi : 10.5802/aif.3554. https://aif.centre-mersenne.org/articles/10.5802/aif.3554/

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