Aperiodic tilings
type: Item
instance of: scholarly article
title: Aperiodic tilings
zbMATH Open document ID: 0879.52011
author: Shahar Mozes
published in: Inventiones Mathematicae
publication date: 1997-07-03T00:00:00Z
review text: The author describes a construction of certain \(X-\)tiling systems. In particular he obtains an aperiodic \(X-\)tiling system for \(X=G/K\) where \(G\) is a semisimple Lie group without compact factors and different from SL\(_2(\mathbb{R}).\) The construction is based on the use of two non-commensurable uniform lattices in \(G\) combined with Mostow rigidity. In the case of \(X=G/K\) with \(G\) being either Sp\((n,1), n\geqq 2\) (here \(X\) is a quaternionic hyperbolic space \(\mathbb{H}\mathbb{H}^n\)), \(F_4^{-20}\) (here \(X\) is the Cayley hyperbolic plane \(\mathbb{C}\)a\(\mathbb{C}^2\)) or a noncompact simple Lie group of rank at least two, a strongly aperiodic tiling system is constructed. The construction is based on the use of two uniform lattices which are disjoint even after arbitrary conjugations and the rigidity results of \textit{P. Pansu} [Ann. Math., II. Ser. 129, No. 1, 1-60 (1989; Zbl 0678.53042)] and \textit{B. Kleiner} and \textit{B. Leeb} [`Rigidity of quasiisometries for symmetric spaces of higher rank', preprint].
Mathematics Subject Classification ID: 52C22
Mathematics Subject Classification ID: 53C25
zbMATH DE Number: 1028193
zbMATH Keywords: tilings in \(n\) dimensions
zbMATH Keywords: tessellation automata
zbMATH Keywords: linear algebraic groups over the quaternions
zbMATH Keywords: tiling affine buildings
zbMATH Keywords: rigidity of structures
reviewed by: Serguey M. Pokas
MaRDI profile type: Publication
Wikidata QID: Q56443073
full work available at URL: s002220050153
OpenAlex ID: W3191581046
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DOI: 10.1007/S002220050153
description: scientific article; zbMATH DE number 1028193