Cohomology of rotational tiling spaces

TY - UNPB

T1 - Cohomology of rotational tiling spaces

AU - Walton, James Jonathan

PY - 2016/9/21

Y1 - 2016/9/21

N2 - A spectral sequence is defined which converges to the \v{C}ech 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 \v{C}ech cohomology of the Euclidean hull of the Penrose tilings.

AB - A spectral sequence is defined which converges to the \v{C}ech 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 \v{C}ech cohomology of the Euclidean hull of the Penrose tilings.

M3 - Preprint

BT - Cohomology of rotational tiling spaces

ER -