A proof of the Gap Labeling Conjecture

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We give a proof of the Gap Labeling Conjecture formulated by J. Bellissard. This gives information about the spectrum of a Schrodinger operator associated to a quasicrystal. The proof makes use of a version of Connes' Index Theorem for Foliations which was introduced by C. Moore and C. Schochet and is appropriate for foliated spaces. These arise naturally in dynamics and are likely to have further applications.
9 pages, Latex file

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K-Theory and Homology, Mathematical Physics, Operator Algebras, 46L87; 52C23

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http://salesiana.dossiersoluciones.com/handle/123456789/64031

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0205102
 http://arxiv.org/abs/math/0205102

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arXiv