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.
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.
Revised:
Accepted:
Published online:
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
@article{AIF_2023__73_4_1533_0, author = {Asano, Tomohiro and Ike, Yuichi}, title = {Sheaf quantization and intersection of rational {Lagrangian} immersions}, journal = {Annales de l'Institut Fourier}, pages = {1533--1587}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {73}, number = {4}, year = {2023}, doi = {10.5802/aif.3554}, language = {en}, url = {https://aif.centre-mersenne.org/articles/10.5802/aif.3554/} }
TY - JOUR AU - Asano, Tomohiro AU - Ike, Yuichi TI - Sheaf quantization and intersection of rational Lagrangian immersions JO - Annales de l'Institut Fourier PY - 2023 SP - 1533 EP - 1587 VL - 73 IS - 4 PB - Association des Annales de l’institut Fourier UR - https://aif.centre-mersenne.org/articles/10.5802/aif.3554/ DO - 10.5802/aif.3554 LA - en ID - AIF_2023__73_4_1533_0 ER -
%0 Journal Article %A Asano, Tomohiro %A Ike, Yuichi %T Sheaf quantization and intersection of rational Lagrangian immersions %J Annales de l'Institut Fourier %D 2023 %P 1533-1587 %V 73 %N 4 %I Association des Annales de l’institut Fourier %U https://aif.centre-mersenne.org/articles/10.5802/aif.3554/ %R 10.5802/aif.3554 %G en %F AIF_2023__73_4_1533_0
Asano, Tomohiro; Ike, Yuichi. Sheaf quantization and intersection of rational Lagrangian immersions. Annales de l'Institut Fourier, Volume 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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