Gap Labelling for Schrödinger Operators on Quasiperiodic Tilings

Abstract

For a large class of tilings, including those which are obtained by the generalized dual method from regular grids, it is shown that their algebra is stably isomorphic to a crossed product with ${\mathbb{Z}}^d$. Penrose tilings belong to this class. This enlarges the class of tilings of which can be shown that a set of possible gap labels is completely determined by an invariant measure on the hull.

13 pages, 1 figure, Latex, KCL-TH-94-10