A Study Of Braids

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A Study of Braids

Author : Kunio Murasugi
Publisher : Springer Science & Business Media
ISBN 13 : 9401593191
Total Pages : 287 pages
Book Rating : 4.4/5 (15 download)

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Book Synopsis A Study of Braids by : Kunio Murasugi

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.

A Study of Braids

Author : Kunio Murasugi
Publisher :
ISBN 13 : 9789401593205
Total Pages : 288 pages
Book Rating : 4.5/5 (932 download)

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Book Synopsis A Study of Braids by : Kunio Murasugi

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.

Braid Groups

Author : Christian Kassel
Publisher : Springer Science & Business Media
ISBN 13 : 0387685480
Total Pages : 349 pages
Book Rating : 4.3/5 (876 download)

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Book Synopsis Braid Groups by : Christian Kassel

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.

Braids, Links, and Mapping Class Groups. (AM-82), Volume 82

Author : Joan S. Birman
Publisher : Princeton University Press
ISBN 13 : 1400881420
Total Pages : 237 pages
Book Rating : 4.4/5 (8 download)

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Book Synopsis Braids, Links, and Mapping Class Groups. (AM-82), Volume 82 by : Joan S. Birman

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.

Braids, Links, and Mapping Class Groups

Author : Joan S. Birman
Publisher : Princeton University Press
ISBN 13 : 9780691081496
Total Pages : 244 pages
Book Rating : 4.0/5 (814 download)

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Book Synopsis Braids, Links, and Mapping Class Groups by : Joan S. Birman

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.

Handbook of Knot Theory

Author : William Menasco
Publisher : Elsevier
ISBN 13 : 9780080459547
Total Pages : 502 pages
Book Rating : 4.4/5 (595 download)

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Book Synopsis Handbook of Knot Theory by : William Menasco

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

Braid and Knot Theory in Dimension Four

Author : Seiichi Kamada
Publisher : American Mathematical Soc.
ISBN 13 : 0821829696
Total Pages : 329 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Braid and Knot Theory in Dimension Four by : Seiichi Kamada

Download or read book Braid and Knot Theory in Dimension Four written by Seiichi Kamada and published by American Mathematical Soc.. This book was released on 2002 with total page 329 pages. Available in PDF, EPUB and Kindle. Book excerpt: Braid theory and knot theory are related via two famous results due to Alexander and Markov. Alexander's theorem states that any knot or link can be put into braid form. Markov's theorem gives necessary and sufficient conditions to conclude that two braids represent the same knot or link. Thus, one can use braid theory to study knot theory and vice versa. In this book, the author generalizes braid theory to dimension four. He develops the theory of surface braids and applies it tostudy surface links. In particular, the generalized Alexander and Markov theorems in dimension four are given. This book is the first to contain a complete proof of the generalized Markov theorem. Surface links are studied via the motion picture method, and some important techniques of this method arestudied. For surface braids, various methods to describe them are introduced and developed: the motion picture method, the chart description, the braid monodromy, and the braid system. These tools are fundamental to understanding and computing invariants of surface braids and surface links. Included is a table of knotted surfaces with a computation of Alexander polynomials. Braid techniques are extended to represent link homotopy classes. The book is geared toward a wide audience, from graduatestudents to specialists. It would make a suitable text for a graduate course and a valuable resource for researchers.

Braids

Author : Joan S. Birman
Publisher : American Mathematical Soc.
ISBN 13 : 0821850881
Total Pages : 766 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Braids by : Joan S. Birman

Download or read book Braids written by Joan S. Birman and published by American Mathematical Soc.. This book was released on 1988 with total page 766 pages. Available in PDF, EPUB and Kindle. Book excerpt: Contains the proceedings of the AMS-IMS-SIAM Joint Summer Research Conference on Artin's Braid Group, held at the University of California, Santa Cruz, in July 1986. This work is suitable for graduate students and researchers who wish to learn more about braids, as well as more experienced workers in this area.

Braids and Self-Distributivity

Author : Patrick Dehornoy
Publisher : Birkhäuser
ISBN 13 : 3034884427
Total Pages : 637 pages
Book Rating : 4.0/5 (348 download)

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Book Synopsis Braids and Self-Distributivity by : Patrick Dehornoy

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.

The Good Braider

Author : Terry Farish
Publisher : Amazon Children's Publishing
ISBN 13 : 9781484430668
Total Pages : 0 pages
Book Rating : 4.4/5 (36 download)

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Book Synopsis The Good Braider by : Terry Farish

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 0 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

Knots, Links, Braids and 3-Manifolds

Author : Viktor Vasilʹevich Prasolov
Publisher : American Mathematical Soc.
ISBN 13 : 0821808982
Total Pages : 250 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Knots, Links, Braids and 3-Manifolds by : Viktor Vasilʹevich Prasolov

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.

Braids and Coverings

Author : Vagn Lundsgaard Hansen
Publisher : Cambridge University Press
ISBN 13 : 9780521387576
Total Pages : 208 pages
Book Rating : 4.3/5 (875 download)

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Book Synopsis Braids and Coverings by : Vagn Lundsgaard Hansen

Download or read book Braids and Coverings written by Vagn Lundsgaard Hansen and published by Cambridge University Press. This book was released on 1989-12-07 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt: Essays develop the elementary theory of Artin Braid groups geometrically and via homotopy theory, discuss the link between knot theory and the combinatorics of braid groups through Markou's Theorem and investigate polynomial covering maps.

A Study of Braids in 3-manifolds

Author : Sofia S. F. Lambropoulou
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (61 download)

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Book Synopsis A Study of Braids in 3-manifolds by : Sofia S. F. Lambropoulou

Download or read book A Study of Braids in 3-manifolds written by Sofia S. F. Lambropoulou and published by . This book was released on 1993 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Quantum Invariants: A Study Of Knots, 3-manifolds, And Their Sets

Author : Tomotada Ohtsuki
Publisher : World Scientific
ISBN 13 : 9814490717
Total Pages : 508 pages
Book Rating : 4.8/5 (144 download)

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Book Synopsis Quantum Invariants: A Study Of Knots, 3-manifolds, And Their Sets by : Tomotada Ohtsuki

Download or read book Quantum Invariants: A Study Of Knots, 3-manifolds, And Their Sets 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.

Badass Braids

Author : Shannon Burns
Publisher :
ISBN 13 : 163106438X
Total Pages : 195 pages
Book Rating : 4.6/5 (31 download)

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Book Synopsis Badass Braids by : Shannon Burns

Download or read book Badass Braids written by Shannon Burns and published by . This book was released on 2018-04-10 with total page 195 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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!

The Collected Papers of Wei-Liang Chow

Author : Shiing-Shen Chern
Publisher : World Scientific
ISBN 13 : 9812776923
Total Pages : 522 pages
Book Rating : 4.8/5 (127 download)

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Book Synopsis The Collected Papers of Wei-Liang Chow by : Shiing-Shen Chern

Download or read book The Collected Papers of Wei-Liang Chow written by Shiing-Shen Chern and published by World Scientific. This book was released on 2002 with total page 522 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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."

Braids

Author : A. Jon Berrick
Publisher : World Scientific
ISBN 13 : 9814291404
Total Pages : 414 pages
Book Rating : 4.8/5 (142 download)

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Book Synopsis Braids by : A. Jon Berrick

Download or read book Braids written by A. Jon Berrick and published by World Scientific. This book was released on 2010 with total page 414 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 given at a Summer School on Braids, at the National University of Singapore's Institute for Mathematical Sciences in June 2007, to an audience of more than thirty international graduate students.