Dans cette Note, nous présentons une solution au problème du label des gaps pour les quasi-cristaux et démontrons ainsi la validité de la conjecture de Bellissard. Nous utilisons le théorème de l'indice mesuré pour les laminations d'un coté et la naturalité du caractère de Chern longitudinal de l'autre.
We give in the present Note a proof of the Bellissard gap-labelling conjecture for quasi-crystals. Our main tools are the measured index theorem for laminations on the one hand, and the naturality of the longitudinal Chern character on the other hand.
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Moulay-Tahar Benameur 1 ; Hervé Oyono-Oyono 2
@article{CRMATH_2002__334_8_667_0,
author = {Moulay-Tahar Benameur and Herv\'e Oyono-Oyono},
title = {Calcul du label des gaps pour les quasi-cristaux},
journal = {Comptes Rendus. Math\'ematique},
pages = {667--670},
publisher = {Elsevier},
volume = {334},
number = {8},
year = {2002},
doi = {10.1016/S1631-073X(02)02312-9},
language = {fr},
}
Moulay-Tahar Benameur; Hervé Oyono-Oyono. Calcul du label des gaps pour les quasi-cristaux. Comptes Rendus. Mathématique, Volume 334 (2002) no. 8, pp. 667-670. doi : 10.1016/S1631-073X(02)02312-9. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/S1631-073X(02)02312-9/
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