Classification of disordered tilings |
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Authors: | Ludwig Balke |
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Institution: | 1. Mathematisches Institut der Universit?t Bonn, Beringstr. 1, 53115, Bonn, Germany
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Abstract: | A tilingT is a disordered realization of a periodic tilingP with symmetry group Γ if we can map the complement of a compact set ofT onto the quotientP/Γ in such a way that this map respects the features of the tilingT andP. We show that the global type of a 2-dimensional tilingT is determined by the periodic tilingP it is a disordered realization of, a conjugacy class of Γ which can be associated toT and a winding number. In some cases, we need in addition some kind of orientation. For higher-dimensional tilings of spaces
which are simply connected at infinity, e.g. ℝ
n
withn≥3, the associated periodic tiling alone is sufficient. |
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Keywords: | 51M20 |
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