Softcover ISBN:  9780821847275 
Product Code:  ULECT/46 
118 pp 
List Price:  $34.00 
MAA Member Price:  $30.60 
AMS Member Price:  $27.20 
Electronic ISBN:  9781470418359 
Product Code:  ULECT/46.E 
118 pp 
List Price:  $32.00 
MAA Member Price:  $28.80 
AMS Member Price:  $25.60 

Book DetailsUniversity Lecture SeriesVolume: 46; 2008MSC: Primary 52; 55;
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 crossreferenced 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.ReadershipGraduate students and research mathematicians interested in topology, dynamical systems, and aperiodic tilings.

Table of Contents

Chapters

Chapter 1. Basic notions

Chapter 2. Tiling spaces and inverse limits

Chapter 3. Cohomology of tilings spaces

Chapter 4. Relaxing the rules I: Rotations

Chapter 5. Patternequivariant cohomology

Chapter 6. Tricks of the trade

Chapter 7. Relaxing the rules II: Tilings without finite local complexity

Appendix A. Solutions to selected exercises


Additional Material

Reviews

Overall, this is a nice text and a welcome addition to the still rather incomplete literature on aperiodic order.
Zentralblatt MATH


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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 crossreferenced 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.
Graduate students and research mathematicians interested in topology, dynamical systems, and aperiodic tilings.

Chapters

Chapter 1. Basic notions

Chapter 2. Tiling spaces and inverse limits

Chapter 3. Cohomology of tilings spaces

Chapter 4. Relaxing the rules I: Rotations

Chapter 5. Patternequivariant cohomology

Chapter 6. Tricks of the trade

Chapter 7. Relaxing the rules II: Tilings without finite local complexity

Appendix A. Solutions to selected exercises

Overall, this is a nice text and a welcome addition to the still rather incomplete literature on aperiodic order.
Zentralblatt MATH