Cohomology groups for spaces of Twelve-Fold Tilings
| Autor: | Nicolas Bédaride, Franz Gähler, Ana G. Lecuona |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2021 |
| Předmět: |
Pure mathematics
Plane (geometry) Group (mathematics) General Mathematics 010102 general mathematics Structure (category theory) 0102 computer and information sciences 01 natural sciences Action (physics) Cohomology Perspective (geometry) 010201 computation theory & mathematics 0101 mathematics Symmetry (geometry) Penrose tiling Mathematics |
| ISSN: | 1073-7928 |
| DOI: | 10.1093/imrn/rnab117 |
| Popis: | We consider tilings of the plane with twelve-fold symmetry obtained by the cut-and-projection method. We compute their cohomology groups using the techniques introduced in [ 9]. To do this, we completely describe the window, the orbits of lines under the group action, and the orbits of 0-singularities. The complete family of generalized twelve-fold tilings can be described using two-parameters and it presents a surprisingly rich cohomological structure. To put this finding into perspective, one should compare our results with the cohomology of the generalized five-fold tilings (more commonly known as generalized Penrose tilings). In this case, the tilings form a one-parameter family, which fits in simply one of the two types of cohomology. |
| Databáze: | OpenAIRE |
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