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Cohomology of rotational tiling spaces

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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Bulletin of the London Mathematical Society Wiley

Cohomology of rotational tiling spaces

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References (15)

Publisher
Wiley
Copyright
© 2017 London Mathematical Society
ISSN
0024-6093
eISSN
1469-2120
DOI
10.1112/blms.12098
Publisher site
See Article on Publisher Site

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 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.

Journal

Bulletin of the London Mathematical SocietyWiley

Published: Dec 1, 2017

Keywords: ; ; ;

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