Integer Cech Cohomology of Icosahedral Projection Tilings

Details Integer Cech Cohomology of Icosahedral Projection Tilings Integer Cech Cohomology of Icosahedral Projection Tilings

2008-09-25

arxiv.org/abs/0809.4442v1

Z. Kristallogr. 223 (2008) 801-804

Mathematics

Dynamical Systems

Scientific paper

10.1524/zkri.2008.1070

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.

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