Cohomology groups for spaces of Twelve-Fold Tilings

Bedaride N, Gähler F, Lecuona AG (2021)
International Mathematics Research Notices: rnab117.

Zeitschriftenaufsatz | E-Veröff. vor dem Druck | Englisch
 
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Autor*in
Bedaride, Nicolas; Gähler, FranzUniBi; Lecuona, Ana G.
Abstract / Bemerkung
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.
Erscheinungsjahr
2021
Zeitschriftentitel
International Mathematics Research Notices
Art.-Nr.
rnab117
ISSN
1073-7928
eISSN
1687-0247
Page URI
https://pub.uni-bielefeld.de/record/2961635

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Bedaride N, Gähler F, Lecuona AG. Cohomology groups for spaces of Twelve-Fold Tilings. International Mathematics Research Notices. 2021: rnab117.
Bedaride, N., Gähler, F., & Lecuona, A. G. (2021). Cohomology groups for spaces of Twelve-Fold Tilings. International Mathematics Research Notices, rnab117. https://doi.org/10.1093/imrn/rnab117
Bedaride, N., Gähler, F., and Lecuona, A. G. (2021). Cohomology groups for spaces of Twelve-Fold Tilings. International Mathematics Research Notices:rnab117.
Bedaride, N., Gähler, F., & Lecuona, A.G., 2021. Cohomology groups for spaces of Twelve-Fold Tilings. International Mathematics Research Notices, : rnab117.
N. Bedaride, F. Gähler, and A.G. Lecuona, “Cohomology groups for spaces of Twelve-Fold Tilings”, International Mathematics Research Notices, 2021, : rnab117.
Bedaride, N., Gähler, F., Lecuona, A.G.: Cohomology groups for spaces of Twelve-Fold Tilings. International Mathematics Research Notices. : rnab117 (2021).
Bedaride, Nicolas, Gähler, Franz, and Lecuona, Ana G. “Cohomology groups for spaces of Twelve-Fold Tilings”. International Mathematics Research Notices (2021): rnab117.

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