توپولوژی فضاهای کاشی‌کاری (سری سخنرانی‌های دانشگاهی)

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

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.

"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."--Jacket Gives an introduction to the topology of tiling spaces. Suitable for graduate students, this title presents a review of the 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.