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A Study of Braids : Mathematics and Its Applications - Kunio Murasugi

A Study of Braids

Mathematics and Its Applications

Hardcover Published: 30th June 1999
ISBN: 9780792357674
Number Of Pages: 277

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This work 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; and the use of braids in the solution of algebraic equations. Dirac's problem and special types of braids termed Mexican plaits are also discussed. Since the book relies on concepts and techniques from algebra and topology, the author 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 aimed at physicists, chemists or biologists 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.

Introduction and Foundations
The Braid Group
Word Problem
Special types of braids
Quotient groups of the braid group
Isotopy of braids
Homotopy braid theory
From knots to braids
Markov's theorem
Knot invariants
Braid groups on surfaces
Algebraic equations
Group theory
Symplectic group
App. IV
App. V
Table of Contents provided by Blackwell. All Rights Reserved.

ISBN: 9780792357674
ISBN-10: 0792357671
Series: Mathematics and Its Applications
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 277
Published: 30th June 1999
Publisher: Springer
Country of Publication: NL
Dimensions (cm): 23.4 x 15.6  x 2.54
Weight (kg): 0.59

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