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Sfb 288 Differential Geometry and Quantum Physics |
Abstract for Sfb Preprint No. 406
Cohomology groups for projection tilings of codimension 2 Franz Gähler und Johannes Kellendonk
The gap-labelling group, which provides the set of possible values of the integrated density of states on gaps in the spectrum of a Hamiltonian describing particles in a tiling, is frequently related to the cohomology of the tiling. We present explicit results for the cohomology of many well-known tilings obtained from the cut and projection method with codimension 2, including the (generalized) Penrose tilings, the Tübingen-Triangle-Tiling, the Ammann-Beenker tiling, and the Socolar tiling.
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