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Everyone knows what braids are, whether they be made of hair, knitting wool, or electrical cables. However, it is not so evident that we can construct a theory about them, i.e. to elaborate a coherent and mathematically interesting corpus of results concerning them. This book demonstrates that there is a resoundingly positive response to this question: braids are fascinating objects, with a variety of rich mathematical properties and potential applications. A special emphasis is placed on the algorithmic aspects and on what can be called the 'calculus of braids', in particular the problem of isotopy. Prerequisites are kept to a minimum, with most results being established from scratch. An appendix at the end of each chapter gives a detailed introduction to the more advanced notions required, including monoids and group presentations. Also included is a range of carefully selected exercises to help the reader test their knowledge, with solutions available.
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Braid. --- Ribbon --- Manufacture.
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Finite groups --- Group extensions (Mathematics) --- Braid theory
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This book is an indispensable guide for anyone seeking to familarize themselves with research in braid groups, configuration spaces and their applications. Starting at the beginning, and assuming only basic topology and group theory, the volume's noted expositors take the reader through the fundamental theory and on to current research and applications in fields as varied as astrophysics, cryptography and robotics. As leading researchers themselves, the authors write enthusiastically about their topics, and include many striking illustrations. The chapters have their origins in tutorials give
Braid theory. --- Representations of groups. --- Algebraic topology.
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Algebraic topology --- Braid theory --- Braids, Theory of --- Theory of braids --- Knot theory --- Low-dimensional topology --- Braid theory. --- Tresses, Théorie des.
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This monograph uses braids to explore dynamics on surfaces, with an eye towards applications to mixing in fluids. The text uses the particular example of taffy pulling devices to represent pseudo-Anosov maps in practice. In addition, its final chapters also briefly discuss current applications in the emerging field of analyzing braids created from trajectory data. While written with beginning graduate students, advanced undergraduates, or practicing applied mathematicians in mind, the book is also suitable for pure mathematicians seeking real-world examples. Readers can benefit from some knowledge of homotopy and homology groups, but these concepts are briefly reviewed. Some familiarity with Matlab is also helpful for the computational examples.
Topology --- Mathematics --- Classical mechanics. Field theory --- topologie --- dynamica --- Braid theory. --- Fluid dynamics. --- Dynamics. --- Dinàmica de fluids
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Braid theory --- Knot theory --- Representations of groups --- Tresses, Théorie des --- Théorie des noeuds --- Représentations de groupes
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Braided fabrics are made by interlacing yarns or strips of fabric. Braiding produces a wide range of structures for technical textile applications from medical sutures to cables for anchoring ships. Written by one of the world's leading experts in the field, the book reviews the basic principles, design and processes used in braiding. The book also discusses specialised braiding techniques such as spiral braiding and lace technology. Provides a solid foundation in the fundamentals of braiding design, processes and machinery Covers the patterning of braided products and the structural and c
Textile fabrics. --- Braid. --- Braiding machinery. --- Textile machinery --- Braiding (Weaving) --- Plaiting --- Weaving --- Cloth --- Fabrics --- Textile industry and fabrics --- Textiles --- Decorative arts --- Dry-goods --- Textile fibers
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