Cohomology of rotational tiling spaces

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 Euclidean pattern‐equivariant (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