Substitutions with vanishing rotationally invariant first cohomology
type: Item
instance of: scholarly article
title: Substitutions with vanishing rotationally invariant first cohomology
zbMATH Open document ID: 1312.52013
DOI: 10.1155/2012/818549
author: Juan G. Escudero
published in: Discrete Dynamics in Nature and Society
publication date: 2012-03-13T00:00:00Z
review text: For any tiling \(X\) we can consider a tiling space \(\Omega_X\) formed by the closure of the translational orbit of one tiling \(X\). If \(X\) has \(N\)-fold rotational symmetry, we can also consider the tiling space \(\overline{\Omega_X}=\Omega_X/Z_N\). Many properties of tiling \(X\) can be described in the terms of cohomologies of the tiling spaces \(\Omega_X\) and \(\overline{\Omega_X}\). In the paper Čech cohomologies of \(\Omega_X\) and \(\overline{\Omega_X}\) for some substitution tilings \(X\) with 3-fold and 9-fold rotational symmetry are computed.
Mathematics Subject Classification ID: 52C20
Mathematics Subject Classification ID: 37B50
Mathematics Subject Classification ID: 05B45
zbMATH DE Number: 6014541
zbMATH Keywords: Čech cohomology
zbMATH Keywords: tiling space
zbMATH Keywords: substitutions
Wikidata QID: Q58700775
reviewed by: Anton Shutov
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2012/818549
OpenAlex ID: W1963799358
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description: scientific article; zbMATH DE number 6014541