**University Lecture Series**

Volume: 46;
2008;
118 pp;
Softcover

MSC: Primary 52; 55;

Print ISBN: 978-0-8218-4727-5

Product Code: ULECT/46

List Price: $32.00

Individual Member Price: $25.60

**Electronic ISBN: 978-1-4704-1835-9
Product Code: ULECT/46.E**

List Price: $32.00

Individual Member Price: $25.60

#### Supplemental Materials

# Topology of Tiling Spaces

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*Lorenzo Sadun*

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.

#### Table of Contents

# Table of Contents

## Topology of Tiling Spaces

- Cover Cover11 free
- Title page i3 free
- Contents v7 free
- Preface vii9 free
- Basic notions 113 free
- Tiling spaces and inverse limits 2133
- Cohomology of tilings spaces 3143
- Relaxing the rules I: Rotations 4557
- Pattern-equivariant cohomology 6173
- Tricks of the trade 7587
- Relaxing the rules II: Tilings without finite local complexity 95107
- Solutions to selected exercises 109121
- Bibliography 117129
- Back Cover Back Cover1131

#### Readership

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

#### Reviews

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

`STML/1`

`MBK/50`

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

`STML/1`

`MBK/50`

-- Zentralblatt MATH