Download or read book A Study of Braids written by Kunio Murasugi and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 287 pages. Available in PDF, EPUB and Kindle. Book excerpt: In Chapter 6, we describe the concept of braid equivalence from the topological point of view. This will lead us to a new concept braid homotopy that is discussed fully in the next chapter. As just mentioned, in Chapter 7, we shall discuss the difference between braid equivalence and braid homotopy. Also in this chapter, we define a homotopy braid invariant that turns out to be the so-called Milnor number. Chapter 8 is a quick review of knot theory, including Alexander's theorem. While, Chapters 9 is devoted to Markov's theorem, which allows the application of this theory to other fields. This was one of the motivations Artin had in mind when he began studying braid theory. In Chapter 10, we discuss the primary applications of braid theory to knot theory, including the introduction of the most important invariants of knot theory, the Alexander polynomial and the Jones polynomial. In Chapter 11, motivated by Dirac's string problem, the ordinary braid group is generalized to the braid groups of various surfaces. We discuss these groups from an intuitive and diagrammatic point of view. In the last short chapter 12, we present without proof one theorem, due to Gorin and Lin [GoL] , that is a surprising application of braid theory to the theory of algebraic equations.
Download or read book Braid Groups written by Christian Kassel and published by Springer Science & Business Media. This book was released on 2008-06-28 with total page 349 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this well-written presentation, motivated by numerous examples and problems, the authors introduce the basic theory of braid groups, highlighting several definitions that show their equivalence; this is followed by a treatment of the relationship between braids, knots and links. Important results then treat the linearity and orderability of the subject. Relevant additional material is included in five large appendices. Braid Groups will serve graduate students and a number of mathematicians coming from diverse disciplines.
Download or read book A Study of Braids written by Kunio Murasugi and published by . This book was released on 1999-06-30 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a comprehensive exposition of the theory of braids, beginning with the basic mathematical definitions and structures. Among the many topics explained in detail are: the braid group for various surfaces; the solution of the word problem for the braid group; braids in the context of knots and links (Alexander's theorem); Markov's theorem and its use in obtaining braid invariants; the connection between the Platonic solids (regular polyhedra) and braids; the use of braids in the solution of algebraic equations. Dirac's problem and special types of braids termed Mexican plaits are also discussed. Audience: Since the book relies on concepts and techniques from algebra and topology, the authors also provide a couple of appendices that cover the necessary material from these two branches of mathematics. Hence, the book is accessible not only to mathematicians but also to anybody who might have an interest in the theory of braids. In particular, as more and more applications of braid theory are found outside the realm of mathematics, this book is ideal for any physicist, chemist or biologist who would like to understand the mathematics of braids. With its use of numerous figures to explain clearly the mathematics, and exercises to solidify the understanding, this book may also be used as a textbook for a course on knots and braids, or as a supplementary textbook for a course on topology or algebra.
Download or read book Braids Links and Mapping Class Groups AM 82 Volume 82 written by Joan S. Birman and published by Princeton University Press. This book was released on 2016-03-02 with total page 237 pages. Available in PDF, EPUB and Kindle. Book excerpt: The central theme of this study is Artin's braid group and the many ways that the notion of a braid has proved to be important in low-dimensional topology. In Chapter 1 the author is concerned with the concept of a braid as a group of motions of points in a manifold. She studies structural and algebraic properties of the braid groups of two manifolds, and derives systems of defining relations for the braid groups of the plane and sphere. In Chapter 2 she focuses on the connections between the classical braid group and the classical knot problem. After reviewing basic results she proceeds to an exploration of some possible implications of the Garside and Markov theorems. Chapter 3 offers discussion of matrix representations of the free group and of subgroups of the automorphism group of the free group. These ideas come to a focus in the difficult open question of whether Burau's matrix representation of the braid group is faithful. Chapter 4 is a broad view of recent results on the connections between braid groups and mapping class groups of surfaces. Chapter 5 contains a brief discussion of the theory of "plats." Research problems are included in an appendix.
Download or read book Braids Links and Mapping Class Groups written by Joan S. Birman and published by Princeton University Press. This book was released on 1974 with total page 244 pages. Available in PDF, EPUB and Kindle. Book excerpt: The central theme of this study is Artin's braid group and the many ways that the notion of a braid has proved to be important in low-dimensional topology. In Chapter 1 the author is concerned with the concept of a braid as a group of motions of points in a manifold. She studies structural and algebraic properties of the braid groups of two manifolds, and derives systems of defining relations for the braid groups of the plane and sphere. In Chapter 2 she focuses on the connections between the classical braid group and the classical knot problem. After reviewing basic results she proceeds to an exploration of some possible implications of the Garside and Markov theorems. Chapter 3 offers discussion of matrix representations of the free group and of subgroups of the automorphism group of the free group. These ideas come to a focus in the difficult open question of whether Burau's matrix representation of the braid group is faithful. Chapter 4 is a broad view of recent results on the connections between braid groups and mapping class groups of surfaces. Chapter 5 contains a brief discussion of the theory of "plats." Research problems are included in an appendix.
Download or read book Handbook of Knot Theory written by William Menasco and published by Elsevier. This book was released on 2005-08-02 with total page 502 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a survey of current topics in the mathematical theory of knots. For a mathematician, a knot is a closed loop in 3-dimensional space: imagine knotting an extension cord and then closing it up by inserting its plug into its outlet. Knot theory is of central importance in pure and applied mathematics, as it stands at a crossroads of topology, combinatorics, algebra, mathematical physics and biochemistry. * Survey of mathematical knot theory * Articles by leading world authorities * Clear exposition, not over-technical * Accessible to readers with undergraduate background in mathematics
Download or read book The Good Braider written by Terry Farish and published by Amazon Children's Publishing. This book was released on 2014-08 with total page 217 pages. Available in PDF, EPUB and Kindle. Book excerpt: Follows Viola as she survives brutality in war-torn Sudan, makes a perilous journey, lives as a refugee in Egypt, and finally reaches Portland, Maine, where her quest for freedom and security is hampered by memories of past horrors and the traditions
Download or read book Quantum Invariants written by Tomotada Ohtsuki and published by World Scientific. This book was released on 2001-12-21 with total page 508 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an extensive and self-contained presentation of quantum and related invariants of knots and 3-manifolds. Polynomial invariants of knots, such as the Jones and Alexander polynomials, are constructed as quantum invariants, i.e. invariants derived from representations of quantum groups and from the monodromy of solutions to the Knizhnik-Zamolodchikov equation. With the introduction of the Kontsevich invariant and the theory of Vassiliev invariants, the quantum invariants become well-organized. Quantum and perturbative invariants, the LMO invariant, and finite type invariants of 3-manifolds are discussed. The Chern–Simons field theory and the Wess–Zumino–Witten model are described as the physical background of the invariants. Contents: Knots and Polynomial InvariantsBraids and Representations of the Braid GroupsOperator Invariants of Tangles via Sliced DiagramsRibbon Hopf Algebras and Invariants of LinksMonodromy Representations of the Braid Groups Derived from the Knizhnik–Zamolodchikov EquationThe Kontsevich InvariantVassiliev InvariantsQuantum Invariants of 3-ManifoldsPerturbative Invariants of Knots and 3-ManifoldsThe LMO InvariantFinite Type Invariants of Integral Homology 3-Spheres Readership: Researchers, lecturers and graduate students in geometry, topology and mathematical physics. Keywords:Kontsevich Invariant;LMO Invariant;Quantum Groups;Knot;3-Manifold;Quantum Invariant;Vassiliev Invariant;Finite Type Invariant;Chord Diagram;Jacobi Diagram;KZ Equation;Chern-Simons TheoryReviews:“This is a nicely written and useful book: I think that the author has done a great job in explaining quantum invariants of knots and 3-manifolds also on an intuitive and well-motivated, organically growing and not too technical level, at the same time however presenting a lot of material ordered by a clear guiding line.”Mathematics Abstracts “Ohtsuki's book is a very valuable addition to the literature. It surveys the full spectrum of work in the area of quantum invariants … Ohtsuk's book is very readable, for he makes an attempt to present the material in as straightforward a way as possible … the presentation here is very clear and should be easily accessible … this is an excellent book which I would recommend to beginners wanting to learn about quantum invariants and to experts alike.”Mathematical Reviews
Download or read book Ordering Braids written by Patrick Dehornoy and published by American Mathematical Soc.. This book was released on 2008 with total page 339 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since the discovery that Artin's braid groups enjoy a left-invariant linear ordering, several different approaches have been used to understand this phenomenon. This text provides an account of those approaches, involving varied objects & domains as combinatorial group theory, self-distributive algebra & finite combinatorics.
Download or read book Erandi s Braids written by Antonio Hernandez Madrigal and published by Penguin. This book was released on 2001-03-19 with total page 33 pages. Available in PDF, EPUB and Kindle. Book excerpt: The yellow dress Erandi wants for her birthday will look beautiful with her long, thick braids. But Mama's fishing net is full of holes, and there isn't enough money to buy both a new net and a birthday dress. The only solution lies with the hair buyers from the city. But Mama's hair isn't nearly as beautiful as Erandi's. Will Erandi have to choose between her birthday present and her braids? This touching tale of love and sacrifice is sprinkled throughout with Spanish words and expressions.
Download or read book Knots Links Braids and 3 Manifolds written by Viktor Vasilʹevich Prasolov and published by American Mathematical Soc.. This book was released on 1997 with total page 250 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an introduction to the remarkable work of Vaughan Jones and Victor Vassiliev on knot and link invariants and its recent modifications and generalizations, including a mathematical treatment of Jones-Witten invariants. The mathematical prerequisites are minimal compared to other monographs in this area. Numerous figures and problems make this book suitable as a graduate level course text or for self-study.
Download or read book Braided Worlds written by Alma Gottlieb and published by University of Chicago Press. This book was released on 2012-09-15 with total page 179 pages. Available in PDF, EPUB and Kindle. Book excerpt: In a compelling mix of literary narrative and ethnography, anthropologist Alma Gottlieb and writer Philip Graham continue the long journey of cultural engagement with the Beng people of Côte d’Ivoire that they first recounted in their award-winning memoir Parallel Worlds. Their commitment over the span of several decades has lent them a rare insight. Braiding their own stories with those of the villagers of Asagbé and Kosangbé, Gottlieb and Graham take turns recounting a host of unexpected dramas with these West African villages, prompting serious questions about the fraught nature of cultural contact. Through events such as a religious leader’s declaration that the authors’ six-year-old son, Nathaniel, is the reincarnation of a revered ancestor, or Graham’s late father being accepted into the Beng afterlife, or the increasing, sometimes dangerous madness of a villager, the authors are forced to reconcile their anthropological and literary gaze with the deepest parts of their personal lives. Along with these intimate dramas, they follow the Beng from times of peace through the times of tragedy that led to Côte d’Ivoire’s recent civil conflicts. From these and many other interweaving narratives—and with the combined strengths of an anthropologist and a literary writer—Braided Worlds examines the impact of postcolonialism, race, and global inequity at the same time that it chronicles a living, breathing village community where two very different worlds meet.
Download or read book The Girl with Braided Hair written by Rasha Adly and published by American University in Cairo Press. This book was released on 2020-11-03 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt: WINNER OF THE SAIF GHOBASH BANIPAL PRIZE FOR ARABIC LITERARY TRANSLATION LONGLISTED FOR THE 2022 DUBLIN LITERARY AWARD LONGLISTED FOR THE INTERNATIONAL PRIZE FOR ARABIC FICTION The lives of two women living centuries apart are connected by an enigmatic painting in this mesmerizing debut based on historical events Art historian, Yasmine, is restoring an unsigned portrait of a strikingly beautiful girl from the Napoleonic Era, when she discovers that the artist has embedded a lock of hair into the painting, something highly unusual. The mysterious painting came into the museum’s possession without record, and Yasmine becomes consumed by the secret concealed within this captivating work. Meanwhile, at the close of the French Campaign in Egypt, sixteen-year-old Zeinab, the daughter of a prominent sheikh, is drawn into French high society when Napoleon himself requests her presence. Enamored by the foreign customs of the Europeans, she finds herself on a dangerous path, one that may ostracize her from her family and culture. Seamlessly merging fiction with history, art, and politics, modern day Cairo with its opulent past, this compelling story of two women caught between worlds and entangled in matters of the heart launches an entrancing new literary voice.
Download or read book A Way to Garden written by Margaret Roach and published by Timber Press. This book was released on 2019-04-30 with total page 321 pages. Available in PDF, EPUB and Kindle. Book excerpt: “A Way to Garden prods us toward that ineffable place where we feel we belong; it’s a guide to living both in and out of the garden.” —The New York Times Book Review For Margaret Roach, gardening is more than a hobby, it’s a calling. Her unique approach, which she calls “horticultural how-to and woo-woo,” is a blend of vital information you need to memorize and intuitive steps you must simply feel and surrender to. In A Way to Garden, Roach imparts decades of garden wisdom on seasonal gardening, ornamental plants, vegetable gardening, design, gardening for wildlife, organic practices, and much more. She also challenges gardeners to think beyond their garden borders and to consider the ways gardening can enrich the world. Brimming with beautiful photographs of Roach’s own garden, A Way to Garden is practical, inspiring, and a must-have for every passionate gardener.
Download or read book Braids and Self Distributivity written by Patrick Dehornoy and published by Birkhäuser. This book was released on 2012-12-06 with total page 637 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the award-winning monograph of the Sunyer i Balaguer Prize 1999. The book presents recently discovered connections between Artin’s braid groups and left self-distributive systems, which are sets equipped with a binary operation satisfying the identity x(yz) = (xy)(xz). Although not a comprehensive course, the exposition is self-contained, and many basic results are established. In particular, the first chapters include a thorough algebraic study of Artin’s braid groups.
Download or read book Tak V Bowes Departed written by Elizabeth Benns and published by . This book was released on 2005 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Tak v bowes departed is an in-depth study of Article 4, British Library Manuscript Harley 2320. This treatise, which dates to the fifteenth century, gives instructions for making forty different braids of varying complexity. Braids such as these were used for a variety of purposes during the medieval period; lacing clothes, purse strings, decorative trim and seal tags. Tak v bowes departed concludes with modern instructions to make each of the braids; original errors have been corrected and noted, and each braid is clearly illustrated for reference. The instructions are provided as both text and diagrams, and include a detailed overview of the technique of 'fingerloop braiding'"--Publisher's web site.
Download or read book The Mathematics of Juggling written by Burkard Polster and published by Springer Science & Business Media. This book was released on 2006-05-26 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: As a juggler the author likes to finish his performances with a stunt that combines props and techniques from a variety of juggling disciplines. Imagine him idling on a giraffe unicycle, while balancing a spinning basketball on a mouth stick, and toss-juggling a sword, a toilet plunger, and a rubber chicken. As a mathematician he is also interested in the treasure trove of beautiful mathematics used to model the different activities in a juggler's repertoire. In this book he provides an intellectually stimulating collection of mostly self-contained mathematical essays that introduce the reader to many elegant results and techniques from a wide range of mathematical disciplines such as combinatorics, graph theory, knot theory, mechanics, differential equations, control theory, and robotics. "The Mathematics of Juggling" is the first comprehensive account summarizing and expanding the results in the literature on juggling tricks and skills, as well as the mathematics behind these tricks and skills. Anybody who is not put off by the word "mathematics" in the title of this book should have a good time reading it.
