Cohomology of rotational tiling spaces

Walton, James

doi:10.1112/blms.12098

Cohomology of rotational tiling spaces

Walton, James

Authors

James Walton

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.

Citation

Walton, J. (2017). Cohomology of rotational tiling spaces. Bulletin of the London Mathematical Society, 49(6), 1013-1027. https://doi.org/10.1112/blms.12098

Journal Article Type	Article
Acceptance Date	Aug 30, 2017
Online Publication Date	Oct 6, 2017
Publication Date	2017-12
Deposit Date	Feb 21, 2017
Publicly Available Date	Sep 1, 2017
Journal	Bulletin of the London Mathematical Society
Print ISSN	0024-6093
Electronic ISSN	1469-2120
Publisher	Wiley
Peer Reviewed	Peer Reviewed
Volume	49
Issue	6
Pages	1013-1027
DOI	https://doi.org/10.1112/blms.12098

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Copyright Statement
This is the accepted version of the following article: Walton, James (2017). Cohomology of rotational tiling spaces. Bulletin of the London Mathematical Society 49(6): 1013-1027, which has been published in final form at https://doi.org/10.1112/blms.12098. This article may be used for non-commercial purposes in accordance With Wiley Terms and Conditions for self-archiving.