Index theory for quasi-crystals. I: Computation of the gap-label group

DOI10.1016/j.jfa.2006.03.029zbMath1134.46046OpenAlexW4366400152MaRDI QIDQ2461235

Hervé Oyono-Oyono, Moulay Tahar Benameur

Publication date: 27 November 2007

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jfa.2006.03.029

zbMATH Keywords

K-theoryquasi-crystalgap-label

Mathematics Subject Classification ID

(K)-theory and operator algebras (including cyclic theory) (46L80) Applications of selfadjoint operator algebras to physics (46L60) Exotic index theories on manifolds (58J22) Noncommutative geometry (à la Connes) (58B34) Quasicrystals and aperiodic tilings in discrete geometry (52C23) Index theory (19K56)

Related Items (11)

Beyond Diophantine Wannier diagrams: gap labelling for Bloch-Landau Hamiltonians ⋮ Bragg spectrum, K-theory, and gap labeling of aperiodic solids ⋮ T-duality simplifies bulk-boundary correspondence ⋮ Gap-labelling conjecture with nonzero magnetic field ⋮ Transverse Laplacians for substitution tilings ⋮ \(C^*\)-algebras of Penrose hyperbolic tilings ⋮ Gabor frames for quasicrystals, \(K\)-theory, and twisted gap labeling ⋮ Integral cohomology of rational projection method patterns ⋮ PV cohomology of the pinwheel tilings, their integer group of coinvariants and gap-labeling ⋮ An index formula for perturbed Dirac operators on Lie manifolds ⋮ Proof of the magnetic gap-labelling conjecture for principal solenoidal tori

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