Knot Theory /

Knot Theory, a lively exposition of the mathematics of knotting, will appeal to a diverse audience from the undergraduate seeking experience outside the traditional range of studies to mathematicians wanting a leisurely introduction to the subject. Graduate students beginning a program of advanced s...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Livingston, Charles
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Cambridge : Cambridge University Press, 2012.
Colección:Carus.
Temas:
Knot theory.
Théorie des nœuds.
Knot theory
Acceso en línea:Texto completo
Tabla de Contenidos:
  • Front Cover
  • Knot Theory
  • Copyright Page
  • Contents
  • Acknowledgements
  • Preface
  • Chapter 1. A Century of Knot Theory
  • Chapter 2. What Is a Knot?
  • Section 1: Wild Knots and Unknottings
  • Section 2: The Definition of a Knot
  • Section 3: Equivalence of Knots, Deformations
  • Section 4: Diagrams and Projections
  • Section 5: Orientations
  • Chapter 3. Combinatorial Techniques
  • Section 1: Reidemeister Moves
  • Section 2: Colorings
  • Section 3: A Generalization of Colorability, mod p Labelings
  • Section 4: Matrices, Labelings, and DeterminantsSection 5: The Alexander Polynomial
  • Chapter 4. Geometric Techniques
  • Section 1: Surfaces and Homeomorphisms
  • Section 2: The Classification of Surfaces
  • Section 3: Seifert Surfaces and the Genus of a Knot
  • Section 4: Surgery on Surfaces
  • Section 5: Connected Sums of Knots and Prime Decompositions
  • Chapter 5. Algebraic Techniques
  • Section 1: Symmetric Groups
  • Section 2: Knots and Groups
  • Section 3: Conjugation and the Labeling Theorem
  • Section 4: Equations in Groups and the Group of a Knot
  • Section 5: The Fundamental GroupChapter 6. Geometry, Algebra, and the Alexander Polynomial
  • Section 1: The Seifert Matrix
  • Section 2: Seifert Matrices and the Alexander Polynomial
  • Section 3: The Signature of a Knot, and other S-Equivalence Invariants
  • Section 4: Knot Groups and the Alexander Polynomial
  • Chapter 7. Numerical Invariants
  • Section 1: Summary of Numerical Invariants
  • Section 2: New Invariants
  • Section 3: Braids and Bridges
  • Section 4: Relations Between the Numerical Invariants
  • Section 5: Independence of Numerical Invariants
  • Chapter 8. Symmetries of KnotsSection 1: Amphicheiral and Reversible Knots
  • Section 2: Periodic Knots
  • Section 3: The Murasugi Conditions
  • Section 4: Periodic Seifert Surfaces and Edmonds' Theorem
  • Section 5: Applications of the Murasugi and Edmonds Conditions
  • Chapter 9. High-Dimensional Knot Theory
  • Section 1: Defining High-dimensional Knots
  • Section 2: Three Dimensions from a 2-dimensional Perspective
  • Section 3: Three-dimensional Cross-sections of a 4-dimensional Knot
  • Section 4: Slice Knots
  • Section 5: The Knot Concordance Group
  • Chapter 10. New Combinatorial TechniquesSection 1: The Conway Polynomial of a Knot
  • Section 2: New Polynomial Invariants
  • Section 3: Kauffman's Bracket Polynomial
  • Appendix 1. Knot Table
  • Appendix 2. Alexander Polynomials
  • References
  • Index

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