2009/05/12 by Hervé Oyono‐Oyono, Oyono-Oyono, Hervé, Samuel Petite +1
Computer Science · Engineering · Mathematics · #Advanced Materials and Mechanics #Advanced Operator Algebra Research #Digital Image Processing Techniques #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric and Algebraic Topology #Mathematics and Applications #Operator Algebras (math.OA)
paper · pdf · doi:10.48550/arxiv.0905.1932
openalex publication_date 2009/05/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.