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Author: Kunio Murasugi
Publisher: Springer Science & Business Media
ISBN: 9401593191
Category : Mathematics
Languages : en
Pages : 287
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Book Description
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.
Author: Kunio Murasugi
Publisher: Springer Science & Business Media
ISBN: 9401593191
Category : Mathematics
Languages : en
Pages : 287
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Book Description
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.
Author: Christian Kassel
Publisher: Springer Science & Business Media
ISBN: 0387685480
Category : Mathematics
Languages : en
Pages : 349
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Book Description
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.
Author: Joan S. Birman
Publisher: Princeton University Press
ISBN: 1400881420
Category : Mathematics
Languages : en
Pages : 241
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Book Description
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.
Author: Joan S. Birman
Publisher: Princeton University Press
ISBN: 9780691081496
Category : Crafts & Hobbies
Languages : en
Pages : 244
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Book Description
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.
Author: Antonio Hernandez Madrigal
Publisher: Penguin
ISBN: 0698118855
Category : Juvenile Fiction
Languages : en
Pages : 33
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Book Description
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.
Author: Ruben Aldrovandi
Publisher: World Scientific
ISBN: 9811248508
Category : Science
Languages : en
Pages : 214
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Book Description
The interface between Physics and Mathematics has been increasingly spotlighted by the discovery of algebraic, geometric, and topological properties in physical phenomena. A profound example is the relation of noncommutative geometry, arising from algebras in mathematics, to the so-called quantum groups in the physical viewpoint. Two apparently unrelated puzzles — the solubility of some lattice models in statistical mechanics and the integrability of differential equations for special problems — are encoded in a common algebraic condition, the Yang-Baxter equation. This backdrop motivates the subject of this book, which reveals Knot Theory as a highly intuitive formalism that is intimately connected to Quantum Field Theory and serves as a basis to String Theory.This book presents a didactic approach to knots, braids, links, and polynomial invariants which are powerful and developing techniques that rise up to the challenges in String Theory, Quantum Field Theory, and Statistical Physics. It introduces readers to Knot Theory and its applications through formal and practical (computational) methods, with clarity, completeness, and minimal demand of requisite knowledge on the subject. As a result, advanced undergraduates in Physics, Mathematics, or Engineering, will find this book an excellent and self-contained guide to the algebraic, geometric, and topological tools for advanced studies in theoretical physics and mathematics.
Author: Shannon Burns
Publisher:
ISBN: 163106438X
Category : Games & Activities
Languages : en
Pages : 195
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Book Description
Recreate the braids, buns, and twists of your favorite historical, sci-fi, and fantasy heroes and heroines with Badass Braids. Step-by-step, illustrated instructions will show you how to make the hairstyles from Game of Thrones, The Hunger Games, Star Trek, Star Wars, The Legend of Zelda, Vikings, The Lord of the Rings, and more. When she’s not studying for her PhD in social neuroscience, Silvousplaits (a.k.a. Shannon Burns) is creating and posting weekly instructional videos on her YouTube channel of DIY hair art that mimics the hairstyles of valiant men and women in the best historical, sci-fi, and fantasy shows and movies. In Badass Braids, Shannon shows you how to transform your hair, step by step. The book covers braids and styles from a full spectrum of fantasy worlds (and galaxies), from ancient adversaries and viking warriors to romantic renegades and sci-fi heroines. With an introduction to the styling techniques for different kinds of basic braids, interviews with behind-the-scenes stylists and actors, and original styles inspired by fan-favorites, you will learn to recreate the hairstyles of Katniss Everdeen (The Hunger Games: Mockingjay), Anne Boleyn (The Tudors), the Norse king Ragnar Lothbrok (Vikings), Daenerys Targaryen (Game of Thrones), and many more. Badass Braids is the perfect gift for geeky men and women of all ages!
Author: Jacqui Carey
Publisher: Interweave
ISBN: 9781596680180
Category : Crafts & Hobbies
Languages : en
Pages : 0
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Book Description
Hundreds of sumptuous braided designs are arranged by structure, from twisted and knotted pieces to more elaborate looped and woven examples. Each braid features a beautiful close-up photograph, materials list, step-by-step instructions, and easy-to-follow color illustrations to guide crafters along. Each technique is explored in-depth, followed by tips on starting and finishing braids and advice for incorporating braids into other textile projects.
Author: Viktor Vasilʹevich Prasolov
Publisher: American Mathematical Soc.
ISBN: 0821808982
Category : Mathematics
Languages : en
Pages : 250
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Book Description
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.
Author: Helen Frost
Publisher: Farrar, Straus and Giroux (BYR)
ISBN: 1466896337
Category : Young Adult Fiction
Languages : en
Pages : 111
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Book Description
Two sisters, Jeannie and Sarah, tell their separate yet tightly interwoven stories in alternating narrative poems. Each sister – Jeannie, who leaves Scotland during the Highland Clearances with her father, mother, and the younger children, and Sarah, who hides so she can stay behind with her grandmother – carries a length of the other's hair braided with her own. The braid binds them together when they are worlds apart and reminds them of who they used to be before they were evicted from the Western Isles, where their family had lived for many generations. The award-winning poet Helen Frost eloquently twists strand over strand of language, braiding the words at the edges of the poems to bring new poetic forms to life while intertwining the destinies of two young girls and the people who cross their paths in this unforgettable novel. An author's note describes the inventive poetic form in detail. The Braid is a 2007 Bank Street - Best Children's Book of the Year.
