Gap Labelling for Schrödinger Operators on Quasiperiodic Tilings

Johannes Kellendonk

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arXiv · cond-mat/9406107

Gap Labelling for Schrödinger Operators on Quasiperiodic Tilings

Johannes Kellendonk

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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 $\Z^d$. 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.

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Johannes Kellendonk. 1994-06-27. Gap Labelling for Schrödinger Operators on Quasiperiodic Tilings. https://arxiv.org/abs/cond-mat/9406107

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