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arXiv · 1609.06606

Cohomology of rotational tiling spaces

James J. Walton
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Abstract

A spectral sequence is defined which converges to the Čech cohomology of the Euclidean hull of a tiling of the plane with Euclidean finite local complexity. The terms of the second page are determined by the so-called ePE homology and ePE cohomology groups of the tiling, and the only potentially non-trivial boundary map has a simple combinatorial description in terms of its local patches. Using this spectral sequence, we compute the Čech cohomology of the Euclidean hull of the Penrose tilings.

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James J. Walton. 2016-09-21. Cohomology of rotational tiling spaces. https://doi.org/10.1112/blms.12098

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