2015 | OriginalPaper | Chapter
On the Noncommutative Geometry of Tilings
Authors : Antoine Julien, Johannes Kellendonk, Jean Savinien
Published in: Mathematics of Aperiodic Order
Publisher: Springer Basel
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We discuss constructions of spectral triples for spaces which are related to subshifts or aperiodic tilings. These spectral triples give rise to distance functions, zeta functions, Laplace operators and K-homology classes. We investigate these objects, and relate their properties to standard notions in tiling theory.