contents.org

• Introduction
• Survey
  • Knot theory
    • Definitions, invariants
    • Polynomial invariants
    • Alternating diagrams, knots, links
    • Seifert surfaces and Seifert’s algorithm
  • Representation theory
  • Theory of braids
    • The Artin braid group
    • Alexander’s theorem
    • Markov’s theorem
    • Burau representation
    • Temperley-Leib algebra
  • Algebraic topology
    • Fundamental group, knot group
    • Homology theory
  • Category theory
    • Categories, functors, natural transformations
    • Categorification
• Resolving the Tait conjectures
  • States-sum model, adequacy, etc.
  • The first Tait conjecture
  • The second Tait conjecture
  • The third Tait conjecture
• Categorification of the Jones polynomial to Khovanov homology
  • The cube category, Bar-Natan category, etc.
• Conclusion