Geodesic
Géométrie et Topologie
The γ-support as a micro-support
Asano, Tomohiro1 ; Guillermou, Stéphane2 ; Humilière, Vincent3  ; Ike, Yuichi4 ; Viterbo, Claude5
1 Faculty of Electrical, Information and Communication Engineering, Institute of Science and Engineering, Kanazawa University, Kakumamachi, Kanazawa, 920-1192, Japan
2 UMR CNRS 6629 du CNRS Laboratoire de Mathématiques Jean LERAY 2 Chemin de la Houssinière, BP 92208, F-44322 NANTES Cedex 3 France
3 Sorbonne Université and Université de Paris, CNRS, IMJ-PRG, F-75005 Paris, France and Institut Universitaire de France
4 Graduate School of Information Science and Technology, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan
5 Université Paris-Saclay, CNRS, Laboratoire de mathématiques d’Orsay, 91405, Orsay, France
Comptes Rendus. Mathématique, Tome 361 (2023) no. G8, pp. 1333-1340

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We prove that for any element L in the completion of the space of smooth compact exact Lagrangian submanifolds of a cotangent bundle equipped with the spectral distance, the γ-support of L coincides with the reduced micro-support of its sheaf quantization. As an application, we give a characterization of the Vichery subdifferential in terms of γ-support.

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DOI : 10.5802/crmath.499

Asano, Tomohiro 1 ; Guillermou, Stéphane 2 ; Humilière, Vincent 3 ; Ike, Yuichi 4 ; Viterbo, Claude 5

1 Faculty of Electrical, Information and Communication Engineering, Institute of Science and Engineering, Kanazawa University, Kakumamachi, Kanazawa, 920-1192, Japan
2 UMR CNRS 6629 du CNRS Laboratoire de Mathématiques Jean LERAY 2 Chemin de la Houssinière, BP 92208, F-44322 NANTES Cedex 3 France
3 Sorbonne Université and Université de Paris, CNRS, IMJ-PRG, F-75005 Paris, France and Institut Universitaire de France
4 Graduate School of Information Science and Technology, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan
5 Université Paris-Saclay, CNRS, Laboratoire de mathématiques d’Orsay, 91405, Orsay, France
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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     title = {The $\gamma $-support as a micro-support},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {1333--1340},
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Asano, Tomohiro; Guillermou, Stéphane; Humilière, Vincent; Ike, Yuichi; Viterbo, Claude. The $\gamma $-support as a micro-support. Comptes Rendus. Mathématique, Tome 361 (2023) no. G8, pp. 1333-1340. doi: 10.5802/crmath.499

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