Topology Of Tiling Spaces

Author : Lorenzo Adlai Sadun
Publisher : American Mathematical Soc.
ISBN 13 : 0821847279
Total Pages : 131 pages
Book Rating : 4.75/5 ( download)

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Download or read book Topology of Tiling Spaces written by Lorenzo Adlai Sadun and published by American Mathematical Soc.. This book was released on 2008 with total page 131 pages. Available in PDF, EPUB and Kindle. Book excerpt: "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."--BOOK JACKET.

Author : Elliott M. Pearl
Publisher : Elsevier
ISBN 13 : 9780080475295
Total Pages : 776 pages
Book Rating : 4.99/5 ( download)

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Download or read book Open Problems in Topology II written by Elliott M. Pearl and published by Elsevier. This book was released on 2011-08-11 with total page 776 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is a collection of surveys of research problems in topology and its applications. The topics covered include general topology, set-theoretic topology, continuum theory, topological algebra, dynamical systems, computational topology and functional analysis. * New surveys of research problems in topology * New perspectives on classic problems * Representative surveys of research groups from all around the world

Author : Sherman Stein
Publisher : Cambridge University Press
ISBN 13 : 9780883850282
Total Pages : 236 pages
Book Rating : 4.81/5 ( download)

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Download or read book Algebra and Tiling written by Sherman Stein and published by Cambridge University Press. This book was released on 1994 with total page 236 pages. Available in PDF, EPUB and Kindle. Book excerpt: A concise investigation into the connections between tiling space problems and algebraic ideas, suitable for undergraduates.

Author : Johannes Kellendonk
Publisher : Birkhäuser
ISBN 13 : 3034809034
Total Pages : 428 pages
Book Rating : 4.30/5 ( download)

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Download or read book Mathematics of Aperiodic Order written by Johannes Kellendonk and published by Birkhäuser. This book was released on 2015-06-05 with total page 428 pages. Available in PDF, EPUB and Kindle. Book excerpt: What is order that is not based on simple repetition, that is, periodicity? How must atoms be arranged in a material so that it diffracts like a quasicrystal? How can we describe aperiodically ordered systems mathematically? Originally triggered by the – later Nobel prize-winning – discovery of quasicrystals, the investigation of aperiodic order has since become a well-established and rapidly evolving field of mathematical research with close ties to a surprising variety of branches of mathematics and physics. This book offers an overview of the state of the art in the field of aperiodic order, presented in carefully selected authoritative surveys. It is intended for non-experts with a general background in mathematics, theoretical physics or computer science, and offers a highly accessible source of first-hand information for all those interested in this rich and exciting field. Topics covered include the mathematical theory of diffraction, the dynamical systems of tilings or Delone sets, their cohomology and non-commutative geometry, the Pisot substitution conjecture, aperiodic Schrödinger operators, and connections to arithmetic number theory.

Author : Shigeki Akiyama
Publisher : Springer Nature
ISBN 13 : 3030576663
Total Pages : 456 pages
Book Rating : 4.60/5 ( download)

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Download or read book Substitution and Tiling Dynamics: Introduction to Self-inducing Structures written by Shigeki Akiyama and published by Springer Nature. This book was released on 2020-12-05 with total page 456 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a panorama of recent developments in the theory of tilings and related dynamical systems. It contains an expanded version of courses given in 2017 at the research school associated with the Jean-Morlet chair program. Tilings have been designed, used and studied for centuries in various contexts. This field grew significantly after the discovery of aperiodic self-similar tilings in the 60s, linked to the proof of the undecidability of the Domino problem, and was driven futher by Dan Shechtman's discovery of quasicrystals in 1984. Tiling problems establish a bridge between the mutually influential fields of geometry, dynamical systems, aperiodic order, computer science, number theory, algebra and logic. The main properties of tiling dynamical systems are covered, with expositions on recent results in self-similarity (and its generalizations, fusions rules and S-adic systems), algebraic developments connected to physics, games and undecidability questions, and the spectrum of substitution tilings.

Author : Colin Adams
Publisher : American Mathematical Society
ISBN 13 : 1470474611
Total Pages : 310 pages
Book Rating : 4.14/5 ( download)

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Download or read book The Tiling Book written by Colin Adams and published by American Mathematical Society. This book was released on 2023-08-28 with total page 310 pages. Available in PDF, EPUB and Kindle. Book excerpt: Tiling theory provides a wonderful opportunity to illustrate both the beauty and utility of mathematics. It has all the relevant ingredients: there are stunning pictures; open problems can be stated without having to spend months providing the necessary background; and there are both deep mathematics and applications. Furthermore, tiling theory happens to be an area where many of the sub-fields of mathematics overlap. Tools can be applied from linear algebra, algebra, analysis, geometry, topology, and combinatorics. As such, it makes for an ideal capstone course for undergraduates or an introductory course for graduate students. This material can also be used for a lower-level course by skipping the more technical sections. In addition, readers from a variety of disciplines can read the book on their own to find out more about this intriguing subject. This book covers the necessary background on tilings and then delves into a variety of fascinating topics in the field, including symmetry groups, random tilings, aperiodic tilings, and quasicrystals. Although primarily focused on tilings of the Euclidean plane, the book also covers tilings of the sphere, hyperbolic plane, and Euclidean 3-space, including knotted tilings. Throughout, the book includes open problems and possible projects for students. Readers will come away with the background necessary to pursue further work in the subject.

Author : Masayuki Asaoka
Publisher : Springer
ISBN 13 : 3034808712
Total Pages : 198 pages
Book Rating : 4.12/5 ( download)

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Download or read book Foliations: Dynamics, Geometry and Topology written by Masayuki Asaoka and published by Springer. This book was released on 2014-10-07 with total page 198 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an introduction to several active research topics in Foliation Theory and its connections with other areas. It contains expository lectures showing the diversity of ideas and methods converging in the study of foliations. The lectures by Aziz El Kacimi Alaoui provide an introduction to Foliation Theory with emphasis on examples and transverse structures. Steven Hurder's lectures apply ideas from smooth dynamical systems to develop useful concepts in the study of foliations: limit sets and cycles for leaves, leafwise geodesic flow, transverse exponents, Pesin Theory and hyperbolic, parabolic and elliptic types of foliations. The lectures by Masayuki Asaoka compute the leafwise cohomology of foliations given by actions of Lie groups, and apply it to describe deformation of those actions. In his lectures, Ken Richardson studies the properties of transverse Dirac operators for Riemannian foliations and compact Lie group actions, and explains a recently proved index formula. Besides students and researchers of Foliation Theory, this book will be interesting for mathematicians interested in the applications to foliations of subjects like Topology of Manifolds, Differential Geometry, Dynamics, Cohomology or Global Analysis.

Author : Charles Radin
Publisher : American Mathematical Soc.
ISBN 13 : 082181933X
Total Pages : 134 pages
Book Rating : 4.33/5 ( download)

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Download or read book Miles of Tiles written by Charles Radin and published by American Mathematical Soc.. This book was released on 1999 with total page 134 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Miles of Tiles" is a mathematics lesson for middle school classes requiring students to calculate the number and cost of tiles needed to cover the floor of the classroom. This lesson includes Internet activities. "Miles of Tiles" is presented as a service of the Link-to-Learn Professional Development Project of Pennsylvania, a state-sponsored educational technology initiative.

Author : Manindra Agrawal
Publisher : Springer Science & Business Media
ISBN 13 : 3540792279
Total Pages : 610 pages
Book Rating : 4.77/5 ( download)

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Download or read book Theory and Applications of Models of Computation written by Manindra Agrawal and published by Springer Science & Business Media. This book was released on 2008-04-08 with total page 610 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 5th International Conference on Theory and Applications of Models of Computation, TAMC 2008, held in Xi'an, China in April 2008. The 48 revised full papers presented together with 2 invited talks and 1 plenary lecture were carefully reviewed and selected from 192 submissions. The papers address current issues of all major areas in computer science, mathematics (especially logic) and the physical sciences - computation, algorithms, complexity and computability theory in particular. With this crossdisciplinary character the conference is given a special flavor and distinction.

Author : W.T. Ingram
Publisher : Springer Science & Business Media
ISBN 13 : 146141797X
Total Pages : 220 pages
Book Rating : 4.72/5 ( download)

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Download or read book Inverse Limits written by W.T. Ingram and published by Springer Science & Business Media. This book was released on 2011-11-06 with total page 220 pages. Available in PDF, EPUB and Kindle. Book excerpt: Inverse limits provide a powerful tool for constructing complicated spaces from simple ones. They also turn the study of a dynamical system consisting of a space and a self-map into a study of a (likely more complicated) space and a self-homeomorphism. In four chapters along with an appendix containing background material the authors develop the theory of inverse limits. The book begins with an introduction through inverse limits on [0,1] before moving to a general treatment of the subject. Special topics in continuum theory complete the book. Although it is not a book on dynamics, the influence of dynamics can be seen throughout; for instance, it includes studies of inverse limits with maps from families of maps that are of interest to dynamicists such as the logistic and the tent families. This book will serve as a useful reference to graduate students and researchers in continuum theory and dynamical systems. Researchers working in applied areas who are discovering inverse limits in their work will also benefit from this book.