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The diffraction spectrum of an aperiodic solid is related to the group ofeigenvalues of the dynamical system associated with the solid. Thoseeigenvalues with continuous eigenfunctions constitute the topological Braggspectrum. We relate the topological Bragg spectrum to the topologicalinvariants (Chern numbers) of the solid and to the gap-labelling group, whichis the group of possible gap labels for the spectrum of a Schr\"odingeroperator describing the electronic motion in the solid.

Bragg spectrum, K-theory and Gap Labelling of aperiodic solids