Walton, J. J. (2017) Cohomology of rotational tiling spaces. Bulletin of the London Mathematical Society, 49(6), pp. 1013-1027. (doi: 10.1112/blms.12098)
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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 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.
| Item Type: | Articles |
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| Additional Information: | This research was supported by EPSRC. |
| Status: | Published |
| Refereed: | Yes |
| Glasgow Author(s) Enlighten ID: | Walton, Dr Jamie |
| Authors: | Walton, J. J. |
| College/School: | College of Science and Engineering > School of Mathematics and Statistics > Mathematics |
| Journal Name: | Bulletin of the London Mathematical Society |
| Publisher: | Wiley |
| ISSN: | 0024-6093 |
| ISSN (Online): | 1469-2120 |
| Published Online: | 06 October 2017 |
| Copyright Holders: | Copyright © 2017 London Mathematical Society |
| First Published: | First published in Bulletin of the London Mathematical Society 49(6): 1013-1027 |
| Publisher Policy: | Reproduced in accordance with the publisher copyright policy |
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