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arXiv · 0905.1932

C*-algebras of Penrose's hyperbolic tilings

Hervé Oyono-Oyono·Samuel Petite
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Abstract

Penrose hyperbolic tilings are tilings of the hyperbolic plane which admit, up to affine transformations a finite number of prototiles. In this paper, we give a complete description of the C*-algebras and of the K-theory for such tilings. Since the continuous hull of these tilings have no transversally invariant measure, these C*-algebras are traceless. Nevertheless, harmonic currents give rise to 3-cyclic cocycles and we discuss in this setting a higher-order version of the gap-labelling.

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BibTeXRIS

Hervé Oyono-Oyono, Samuel Petite. 2010-06-08. C*-algebras of Penrose's hyperbolic tilings. https://arxiv.org/abs/0905.1932

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