Projects per year
Abstract
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 socalled ePE homology and ePE cohomology groups of the tiling, and the only potentially nontrivial 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.
Original language  English 

Number of pages  16 
Publication status  Published  21 Sep 2016 
Projects
 2 Finished

Gaps theorems and statistics of patterns in quasicrystals
1/07/15 → 30/06/18
Project: Research project (funded) › Research

Diophantine approximation, chromatic number, and equivalence classes of separated nets
10/10/13 → 9/07/15
Project: Research project (funded) › Research