Integral cohomology of rational projection method patterns

• Published in: arXiv.org
• Main Authors: Gaehler, Franz, Hunton, John, Kellendonk, Johannes
• Format: Paper Journal Article
• Language: English
• Published: Ithaca Cornell University Library, arXiv.org 26.10.2012
• Subjects: Euclidean geometry; Euclidean space; Homology; Icosahedral phase; Integrals; Invariants; Mathematical analysis; Mathematics - Algebraic Topology; Mathematics - K-Theory and Homology; Mathematics - Mathematical Physics; Periodic structures; Physics - Mathematical Physics; Quantum mechanics; Quasicrystals; Tiling

We study the cohomology and hence \(K\)-theory of the aperiodic tilings formed by the so called 'cut and project' method, i.e., patterns in \(d\) dimensional Euclidean space which arise as sections of higher dimensional, periodic structures. They form one of the key families of patterns us...