Integer Cech cohomology of icosahedral projection tilings
| Autor: | John Hunton, Franz Gähler, Johannes Kellendonk |
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| Rok vydání: | 2008 |
| Předmět: |
Torsion
Icosahedral symmetry Dimension (graph theory) Dynamical Systems (math.DS) Codimension Condensed Matter Physics Cohomology Inorganic Chemistry Combinatorics Tilings Integer Projection (mathematics) Mathematics::K-Theory and Homology FOS: Mathematics Torsion (algebra) Algebraic Topology (math.AT) General Materials Science Mathematics - Algebraic Topology Mathematics - Dynamical Systems Čech cohomology Mathematics |
| Zdroj: | Zeitschrift für Kristallographie. 223:801-804 |
| ISSN: | 0044-2968 |
| DOI: | 10.1524/zkri.2008.1070 |
| Popis: | The integer Cech cohomology of canonical projection tilings of dimension three and codimension three is derived. These formulae are then evaluated for several icosahedral tilings known from the literature. Rather surprisingly, the cohomologies of all these tilings turn out to have torsion. This is the case even for the Danzer tiling, which is, in some sense, the simplest of all icosahedral tilings. This result is in contrast to the case of two-dimensional canonical projection tilings, where many examples without torsion are known. |
| Databáze: | OpenAIRE |
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