Zur Startseite gehen
0,00 €*
Cover: 9780792357674 | A Study of Braids | B. Kurpita (u. a.) | Buch | x | Englisch | 1999
Dekorationsartikel gehören nicht zum Leistungsumfang.
A Study of Braids
Buch von B. Kurpita (u. a.)
Sprache: Englisch

53,49 €*

inkl. MwSt.

Versandkostenfrei per Post / DHL

Aktuell nicht verfügbar

Kategorien:
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.- 1. Various types of braids.- 2. A definition of a braid.- 3. An elementary move and braid equivalence.- 4. Braid projection.- 5. Braid permutation, pure braid.- 2. The Braid Group.- 1. Defunition of the braid group.- 2. A presentation for the braid group.- 3. The completeness of the relations.- 4. Elementary properties of the braid group.- 5. A braid invariant.- 3. Word Problem.- 1. Word problem for the braid group.- 2. A solution of the word problem.- 3. A presentation for the pure n-braid group.- 4. Special types of braids.- 1. Mexicar plaits.- 2. Generators of the Mexican plaits.- 3. An algorithm for Mexican plaits.- 4. Examples of the use of the algorithm.- 5. Quotient groups of the braid group.- 1. Sywumetric group and the braid group.- 2. Platoric solids and quotient groups of Bn.- 3. Finite quotient groups of B3.- 4. The firite quotient group B4(3).- 5. The finite quotient group B5(3).- 6. Isotopy of braids.- 1. Equivalence and isotopy.- 2. Words.- 3. Several interpretations of equivalence.- 4. Milnor invariant.- 7. Homotopy braid theory.- 1. Homotopy.- 2. Tangles and homotopy.- 3. Homotopy braid group.- 4. Homotopy braid invariants.- 5. Tangles and braids.- 8. Grom knots to braids.- 1. Knot theory - a quick review.- 2. Quasi-braids.- 3. Braided links.- 4. Alexander's theorem.- 5. Knot invariants via braid invariants.- 9. Markov's theorem.- 1. A theorem due to Markov.- 2. Proof of Markov's theorem - I.- 3. Proof of Markov's theorem - II.- 4. Applications.- 10. Knot invariants.- 1. Burau representation.- 2. Alexander polynomial.- 3. Jones polynomial.- 4. Alexander versus Jones.- 11. Braid groups on surfaces.- 1. Divac's Problem.- 2. Braid group on S2.- 3. Braid group on the surface F.- 4. Braid group on P2.- 5. Braidgroup on T2.- 6. Word problem for Bn(S2).- 12. Algebraic equations.- 1. Configuration spaces.- 2. Complete solvability.- Appendix I - Group theory.- 1. Equivalence relation.- 2. Groups and a bit of ring theory.- 3. Free group.- 4. Presentations of groups.- 5. Word problem.- 6. Reidemeister-Schreier method, presentation of a subgroup.- 7. Triangle groups.- Appendix II - Topology.- 1. Fundamental concepts of Topology.- 2. Homotopy.- 3. Fundamental group.- 4. Manifolds.- Appendix III - Symplectic group.- 1. Symplectic group.- Appendix IV.- Appendix V.
Details
Erscheinungsjahr: 1999
Fachbereich: Geometrie
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Buch
Reihe: Mathematics and Its Applications
Inhalt: x
277 S.
ISBN-13: 9780792357674
ISBN-10: 0792357671
Sprache: Englisch
Ausstattung / Beilage: HC runder Rücken kaschiert
Einband: Gebunden
Autor: Kurpita, B.
Murasugi, Kunio
Hersteller: Springer Netherland
Springer Netherlands
Mathematics and Its Applications
Maße: 241 x 160 x 20 mm
Von/Mit: B. Kurpita (u. a.)
Erscheinungsdatum: 30.06.1999
Gewicht: 0,606 kg
Artikel-ID: 102550255
Inhaltsverzeichnis
1. Introduction & Foundations.- 1. Various types of braids.- 2. A definition of a braid.- 3. An elementary move and braid equivalence.- 4. Braid projection.- 5. Braid permutation, pure braid.- 2. The Braid Group.- 1. Defunition of the braid group.- 2. A presentation for the braid group.- 3. The completeness of the relations.- 4. Elementary properties of the braid group.- 5. A braid invariant.- 3. Word Problem.- 1. Word problem for the braid group.- 2. A solution of the word problem.- 3. A presentation for the pure n-braid group.- 4. Special types of braids.- 1. Mexicar plaits.- 2. Generators of the Mexican plaits.- 3. An algorithm for Mexican plaits.- 4. Examples of the use of the algorithm.- 5. Quotient groups of the braid group.- 1. Sywumetric group and the braid group.- 2. Platoric solids and quotient groups of Bn.- 3. Finite quotient groups of B3.- 4. The firite quotient group B4(3).- 5. The finite quotient group B5(3).- 6. Isotopy of braids.- 1. Equivalence and isotopy.- 2. Words.- 3. Several interpretations of equivalence.- 4. Milnor invariant.- 7. Homotopy braid theory.- 1. Homotopy.- 2. Tangles and homotopy.- 3. Homotopy braid group.- 4. Homotopy braid invariants.- 5. Tangles and braids.- 8. Grom knots to braids.- 1. Knot theory - a quick review.- 2. Quasi-braids.- 3. Braided links.- 4. Alexander's theorem.- 5. Knot invariants via braid invariants.- 9. Markov's theorem.- 1. A theorem due to Markov.- 2. Proof of Markov's theorem - I.- 3. Proof of Markov's theorem - II.- 4. Applications.- 10. Knot invariants.- 1. Burau representation.- 2. Alexander polynomial.- 3. Jones polynomial.- 4. Alexander versus Jones.- 11. Braid groups on surfaces.- 1. Divac's Problem.- 2. Braid group on S2.- 3. Braid group on the surface F.- 4. Braid group on P2.- 5. Braidgroup on T2.- 6. Word problem for Bn(S2).- 12. Algebraic equations.- 1. Configuration spaces.- 2. Complete solvability.- Appendix I - Group theory.- 1. Equivalence relation.- 2. Groups and a bit of ring theory.- 3. Free group.- 4. Presentations of groups.- 5. Word problem.- 6. Reidemeister-Schreier method, presentation of a subgroup.- 7. Triangle groups.- Appendix II - Topology.- 1. Fundamental concepts of Topology.- 2. Homotopy.- 3. Fundamental group.- 4. Manifolds.- Appendix III - Symplectic group.- 1. Symplectic group.- Appendix IV.- Appendix V.
Details
Erscheinungsjahr: 1999
Fachbereich: Geometrie
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Buch
Reihe: Mathematics and Its Applications
Inhalt: x
277 S.
ISBN-13: 9780792357674
ISBN-10: 0792357671
Sprache: Englisch
Ausstattung / Beilage: HC runder Rücken kaschiert
Einband: Gebunden
Autor: Kurpita, B.
Murasugi, Kunio
Hersteller: Springer Netherland
Springer Netherlands
Mathematics and Its Applications
Maße: 241 x 160 x 20 mm
Von/Mit: B. Kurpita (u. a.)
Erscheinungsdatum: 30.06.1999
Gewicht: 0,606 kg
Artikel-ID: 102550255
Warnhinweis

Ähnliche Produkte

Ähnliche Produkte

Taschenbuch
Cover: 9780521701754 | Algebraic Cycles and Motives, Volume 2 | Chris Peters | Taschenbuch
Algebraic Cycles and Motives, Volume 2
EAN: 9780521701754
Sprache: Englisch
Von/Mit: Chris Peters

75,50 €*

Aktuell nicht verfügbar

Taschenbuch
Cover: 9783540560111 | Mathematical Research Today and Tomorrow | Manuel Castellet (u. a.)
Mathematical Research Today and Tomorrow
Viewpoints of Seven Fields Medalists. Lectures given at the Institut d'Estudis Catalans, Barcelona, Spain, June 1991
EAN: 9783540560111
Sprache: Englisch
Von/Mit: Carles Casacuberta (u. a.)

37,40 €*

Aktuell nicht verfügbar

Taschenbuch
Cover: 9783319110288 | Berkovich Spaces and Applications | Antoine Ducros (u. a.) | Buch
Berkovich Spaces and Applications
EAN: 9783319110288
Sprache: Englisch
Von/Mit: Antoine Ducros (u. a.)

85,59 €*

Aktuell nicht verfügbar

Taschenbuch
Cover: 9781461264750 | Geometric Phases in Classical and Quantum Mechanics | Taschenbuch
Geometric Phases in Classical and Quantum Mechanics
EAN: 9781461264750
Sprache: Englisch
Von/Mit: Andrzej Jamiolkowski (u. a.)

85,59 €*

Aktuell nicht verfügbar

Taschenbuch
Cover: 9780521189811 | Fractals, Scaling and Growth Far from Equilibrium | Paul Meakin | Buch
Fractals, Scaling and Growth Far from Equilibrium
EAN: 9780521189811
Sprache: Englisch
Von/Mit: Paul Meakin

94,00 €*

Aktuell nicht verfügbar

Taschenbuch
Cover: 9783662502419 | Triangulations | Structures for Algorithms and Applications | Buch
Triangulations
Structures for Algorithms and Applications
EAN: 9783662502419
Sprache: Englisch
Von/Mit: Jesus De Loera (u. a.)

85,59 €*

Aktuell nicht verfügbar

Taschenbuch
Cover: 9783030807313 | A Readable Introduction to Real Mathematics | Daniel Rosenthal (u. a.)
A Readable Introduction to Real Mathematics
EAN: 9783030807313
Sprache: Englisch
Von/Mit: Daniel Rosenthal (u. a.)

53,49 €*

Aktuell nicht verfügbar

Taschenbuch
Cover: 9781434916099 | Some Sine and Cosine Identities Obtained from Pascal's Triangle | Buch
Some Sine and Cosine Identities Obtained from Pascal's Triangle
EAN: 9781434916099
Sprache: Englisch
Von/Mit: Christopher White

10,90 €*

Aktuell nicht verfügbar

Taschenbuch
Cover: 9780367766801 | Student Solutions Manual for Gallian's Contemporary Abstract Algebra
Student Solutions Manual for Gallian's Contemporary Abstract Algebra
EAN: 9780367766801
Sprache: Englisch
Von/Mit: Joseph A. Gallian

71,90 €*

Aktuell nicht verfügbar

Taschenbuch
Cover: 9783111085401 | Lectures on Linear Algebra and its Applications | Philip Korman | Buch
Lectures on Linear Algebra and its Applications
EAN: 9783111085401
Sprache: Englisch
Von/Mit: Philip Korman

63,95 €*

Lieferzeit 1-2 Wochen

Diese Website verwendet Cookies, um eine bestmögliche Erfahrung bieten zu können. Mehr Informationen ...