Bédaride, N., Gähler, F. and Lecuona, A. G. (2022) Cohomology Groups for Spaces of Twelve-Fold Tilings. International Mathematics Research Notices, 2022(18), pp. 14181-14254. (doi: 10.1093/imrn/rnab117)
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Abstract
We consider tilings of the plane with twelve-fold symmetry obtained by the cutand-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.
Item Type: | Articles |
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Additional Information: | Funding: This work was supported by the German Research Foundation [CRC 1283 to F.G.]; and the Engineering and Physical Sciences Research Council [EP/T028408/1 to A.G.L.]. |
Status: | Published |
Refereed: | Yes |
Glasgow Author(s) Enlighten ID: | Garcia Lecuona, Professor Ana |
Authors: | Bédaride, N., Gähler, F., and Lecuona, A. G. |
College/School: | College of Science and Engineering > School of Mathematics and Statistics > Mathematics |
Journal Name: | International Mathematics Research Notices |
Publisher: | Oxford University Press |
ISSN: | 1073-7928 |
ISSN (Online): | 1687-0247 |
Published Online: | 02 June 2021 |
Copyright Holders: | Copyright © 2021 The Authors |
First Published: | First published in International Mathematics Research Notices 2022(18): 14181-14254 |
Publisher Policy: | Reproduced under a Creative Commons licence |
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