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Author: Jean-Luc Thiffeault
Publisher: Springer Nature
ISBN: 3031047907
Category : Mathematics
Languages : en
Pages : 147
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Book Description
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.
Author: Jean-Luc Thiffeault
Publisher: Springer Nature
ISBN: 3031047907
Category : Mathematics
Languages : en
Pages : 147
Get Book Here
Book Description
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.
Author: Wojciech Tomasz Wójcik
Publisher:
ISBN: 9789090227634
Category :
Languages : en
Pages : 127
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Book Description
Author: Vagn Lundsgaard Hansen
Publisher: Cambridge University Press
ISBN: 9780521387576
Category : Mathematics
Languages : en
Pages : 208
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Book Description
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.
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: Joan S. Birman
Publisher: American Mathematical Soc.
ISBN: 0821850881
Category : Mathematics
Languages : en
Pages : 766
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Book Description
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.
Author: A. Jon Berrick
Publisher: World Scientific
ISBN: 9814291412
Category : Mathematics
Languages : en
Pages : 414
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Book Description
Tutorial on the braid groups / Dale Rolfsen -- Simplicial objects and homotopy groups / Jie Wu -- Introduction to configuration spaces and their applications / Frederick R. Cohen -- Configuration spaces, braids, and robotics / Robert Ghrist -- Braids and magnetic fields / Mitchell A. Berger -- Braid group cryptography / David Garber
Author: Joelle Bearstail
Publisher: Mascot Books
ISBN: 9781645434979
Category :
Languages : en
Pages : 38
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Book Description
Bear and his friend Ben feel like they are living two lives: one, where native traditions--like long hair--are a crucial part of their identities, and the other, where indigenous expressions are mocked and treated with ignorance. When the boys encounter bullying because of the braids they wear, these two worlds collide. Seeking guidance from his beloved grandma, Bear confides his doubts and questions himself and his heritage. Bear's grandma knows about the strength it takes to overcome hardships, and with her help, Bear and Ben develop a plan to strengthen their connection to their roots while also bridging the gap between their schoolmates and their families. Seamlessly blending discussions of modern indigeneity and universal experiences of bullying and resilience, Bear's Braid is an essential and of-the-moment book that belongs on every bookshelf, and fits in easily with the classics of social justice children's literature.
Author: Patrick Dehornoy
Publisher: Birkhäuser
ISBN: 3034884427
Category : Mathematics
Languages : en
Pages : 637
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Book Description
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.
Author: Jacqui Carey
Publisher:
ISBN: 9780952322542
Category : Braid
Languages : en
Pages : 56
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Book Description
Author: Joan S. Birman
Publisher: Princeton University Press
ISBN: 1400881420
Category : Mathematics
Languages : en
Pages : 237
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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.
