Bibliographic Information

A study of braids

by Kunio Murasugi and Bohdan I. Kurpita

(Mathematics and its applications, v. 484)

Kluwer Academic, c1999

  • : Softcover

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Note

Includes bibliographical references and index

"Softcover reprint of the hardcover 1st edition 1999"--T.p. verso

Description and Table of Contents

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.

Table of Contents

1. Introduction & Foundations. 2. The Braid Group. 3. World Problem. 4. Special types of braids. 5. Quotient groups of the braid group. 6. Isotopy of braids. 7. Homotopy braid theory. 8. From knots to braids. 9. Markov's theorem. 10. Knot invariants. 11. Braid groups on surfaces. 12. Algebraic equations. Appendix I: Group theory. Appendix II: Topology. Appendix III: Symplectic group. Appendix IV. Appendix V. Bibliography. Index.

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Details

  • NCID
    BA42474683
  • ISBN
    • 0792357671
    • 9789048152452
  • LCCN
    99027052
  • Country Code
    ne
  • Title Language Code
    eng
  • Text Language Code
    eng
  • Place of Publication
    Dordrecht
  • Pages/Volumes
    x, 272 p.
  • Size
    25 cm
  • Classification
  • Subject Headings
  • Parent Bibliography ID
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