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Cover: 9789048152452 | A Study of Braids | B. Kurpita (u. a.) | Taschenbuch | Paperback | x
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A Study of Braids
Taschenbuch von B. Kurpita (u. a.)
Sprache: Englisch

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Beschreibung
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.
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.
Inhaltsverzeichnis
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.
Details
Erscheinungsjahr: 2010
Fachbereich: Geometrie
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Taschenbuch
Reihe: Mathematics and Its Applications
Inhalt: x
277 S.
ISBN-13: 9789048152452
ISBN-10: 9048152453
Sprache: Englisch
Ausstattung / Beilage: Paperback
Einband: Kartoniert / Broschiert
Autor: Kurpita, B.
Murasugi, Kunio
Auflage: Softcover reprint of hardcover 1st ed. 1999
Hersteller: Springer Netherland
Springer Netherlands
Mathematics and Its Applications
Maße: 235 x 155 x 16 mm
Von/Mit: B. Kurpita (u. a.)
Erscheinungsdatum: 15.12.2010
Gewicht: 0,441 kg
Artikel-ID: 107246275
Inhaltsverzeichnis
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.
Details
Erscheinungsjahr: 2010
Fachbereich: Geometrie
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Taschenbuch
Reihe: Mathematics and Its Applications
Inhalt: x
277 S.
ISBN-13: 9789048152452
ISBN-10: 9048152453
Sprache: Englisch
Ausstattung / Beilage: Paperback
Einband: Kartoniert / Broschiert
Autor: Kurpita, B.
Murasugi, Kunio
Auflage: Softcover reprint of hardcover 1st ed. 1999
Hersteller: Springer Netherland
Springer Netherlands
Mathematics and Its Applications
Maße: 235 x 155 x 16 mm
Von/Mit: B. Kurpita (u. a.)
Erscheinungsdatum: 15.12.2010
Gewicht: 0,441 kg
Artikel-ID: 107246275
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