A Study Of Braids
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| Author | : Kunio Murasugi |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 287 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 9401593191 |
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 |
| Total Pages | : 349 |
| Release | : 2008-06-28 |
| Genre | : Mathematics |
| ISBN | : 0387685480 |
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 |
| Total Pages | : 241 |
| Release | : 2016-03-02 |
| Genre | : Mathematics |
| ISBN | : 1400881420 |
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 | : William Menasco |
| Publisher | : Elsevier |
| Total Pages | : 502 |
| Release | : 2005-08-02 |
| Genre | : Mathematics |
| ISBN | : 9780080459547 |
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
| Author | : Joan S. Birman |
| Publisher | : Princeton University Press |
| Total Pages | : 244 |
| Release | : 1974 |
| Genre | : Crafts & Hobbies |
| ISBN | : 9780691081496 |
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 | : Tomotada Ohtsuki |
| Publisher | : World Scientific |
| Total Pages | : 508 |
| Release | : 2001-12-21 |
| Genre | : Mathematics |
| ISBN | : 9814490717 |
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.
| Author | : Viktor Vasilʹevich Prasolov |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 250 |
| Release | : 1997 |
| Genre | : Mathematics |
| ISBN | : 0821808982 |
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 | : Shiing-Shen Chern |
| Publisher | : World Scientific |
| Total Pages | : 522 |
| Release | : 2002 |
| Genre | : Mathematics |
| ISBN | : 9812776923 |
This invaluable book contains the collected papers of Prof Wei-Liang Chow, an original and versatile mathematician of the 20th Century. Prof Chow''s name has become a household word in mathematics because of the Chow ring, Chow coordinates, and Chow''s theorem on analytic sets in projective spaces. The Chow ring has many advantages and is widely used in intersection theory of algebraic geometry. Chow coordinates have been a very versatile tool in many aspects of algebraic geometry. Chow''s theorem OCo that a compact analytic variety in a projective space is algebraic OCo is justly famous; it shows the close analogy between algebraic geometry and algebraic number theory.About Professor Wei-Liang ChowThe long and distinguished career of Prof Wei-Liang Chow (1911OCo95) as a mathematician began in China with professorships at the National Central University in Nanking (1936OCo37) and the National Tung-Chi University in Shanghai (1946OCo47), and ultimately led him to the United States, where he joined the mathematics faculty of Johns Hopkins University in Baltimore, Maryland, first as an associate professor from 1948 to 1950, then as a full professor from 1950 until his retirement in 1977.In addition to serving as chairman of the mathematics department at Johns Hopkins from 1955 to 1965, he was Editor-in-Chief of the American Journal of Mathematics from 1953 to 1977."
| Author | : Terry Farish |
| Publisher | : Amazon Children's Publishing |
| Total Pages | : 0 |
| Release | : 2014-08 |
| Genre | : |
| ISBN | : 9781484430668 |
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
| Author | : Shannon Burns |
| Publisher | : |
| Total Pages | : 195 |
| Release | : 2018-04-10 |
| Genre | : Games & Activities |
| ISBN | : 163106438X |
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!
