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Topology of tiling spaces

Aperiodic tilings are interesting to mathematicians and scientists for both theoretical and practical reasons. The serious study of aperiodic tilings began as a solution to a problem in logic. Simpler aperiodic tilings eventually revealed hidden "symmetries" that were previously considered...

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Detalles Bibliográficos
Autor principal: Sadun, Lorenzo
Lenguaje:eng
Publicado: American Mathematical Society 2008
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Acceso en línea:http://cds.cern.ch/record/2623071
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author Sadun, Lorenzo
author_facet Sadun, Lorenzo
author_sort Sadun, Lorenzo
collection CERN
description Aperiodic tilings are interesting to mathematicians and scientists for both theoretical and practical reasons. The serious study of aperiodic tilings began as a solution to a problem in logic. Simpler aperiodic tilings eventually revealed hidden "symmetries" that were previously considered impossible, while the tilings themselves were quite striking. The discovery of quasicrystals showed that such aperiodicity actually occurs in nature and led to advances in materials science. Many properties of aperiodic tilings can be discerned by studying one tiling at a time. However, by studying families of tilings, further properties are revealed. This broader study naturally leads to the topology of tiling spaces. This book is an introduction to the topology of tiling spaces, with a target audience of graduate students who wish to learn about the interface of topology with aperiodic order. It isn't a comprehensive and cross-referenced tome about everything having to do with tilings, which would be too big, too hard to read, and far too hard to write! Rather, it is a review of the explosion of recent work on tiling spaces as inverse limits, on the cohomology of tiling spaces, on substitution tilings and the role of rotations, and on tilings that do not have finite local complexity. Powerful computational techniques have been developed, as have new ways of thinking about tiling spaces. The text contains a generous supply of examples and exercises.
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spelling cern-26230712021-04-21T18:47:45Zhttp://cds.cern.ch/record/2623071engSadun, LorenzoTopology of tiling spacesMathematical Physics and MathematicsAperiodic tilings are interesting to mathematicians and scientists for both theoretical and practical reasons. The serious study of aperiodic tilings began as a solution to a problem in logic. Simpler aperiodic tilings eventually revealed hidden "symmetries" that were previously considered impossible, while the tilings themselves were quite striking. The discovery of quasicrystals showed that such aperiodicity actually occurs in nature and led to advances in materials science. Many properties of aperiodic tilings can be discerned by studying one tiling at a time. However, by studying families of tilings, further properties are revealed. This broader study naturally leads to the topology of tiling spaces. This book is an introduction to the topology of tiling spaces, with a target audience of graduate students who wish to learn about the interface of topology with aperiodic order. It isn't a comprehensive and cross-referenced tome about everything having to do with tilings, which would be too big, too hard to read, and far too hard to write! Rather, it is a review of the explosion of recent work on tiling spaces as inverse limits, on the cohomology of tiling spaces, on substitution tilings and the role of rotations, and on tilings that do not have finite local complexity. Powerful computational techniques have been developed, as have new ways of thinking about tiling spaces. The text contains a generous supply of examples and exercises.American Mathematical Societyoai:cds.cern.ch:26230712008
spellingShingle Mathematical Physics and Mathematics
Sadun, Lorenzo
Topology of tiling spaces
title Topology of tiling spaces
title_full Topology of tiling spaces
title_fullStr Topology of tiling spaces
title_full_unstemmed Topology of tiling spaces
title_short Topology of tiling spaces
title_sort topology of tiling spaces
topic Mathematical Physics and Mathematics
url http://cds.cern.ch/record/2623071
work_keys_str_mv AT sadunlorenzo topologyoftilingspaces