2002/05/10 by Jerome Kaminker, Kaminker, Jerome, Ian Putnam +1
Mathematics · Physics and Astronomy · #46L87 #52C23 #FOS: Mathematics #FOS: Physical sciences #K-Theory and Homology (math.KT) #Mathematical Physics (math-ph) #Operator Algebras (math.OA) #math-ph #math.KT #math.MP #math.OA #msc:46L87 #msc:52C23
paper · pdf · doi:10.48550/arxiv.math/0205102
9 pages, Latex file
arxiv created 2002/05/10 · arxiv updated 2009/11/30
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.