Contents

• Introduction
  • What are these web pages about
  • Target readers
  • Other sources of data used in our calculations
  • Comments on history
  
  
• Knot Diagrams and Reidemeister Moves
  • Knot Diagrams
  • Reidemeister Moves
  • Knotted Surface Diagrams and Their Moves
  
  
• Quandles and Their Colorings of Knot Diagrams
  • Racks and Quandles
  • Colorings of Knot Diagrams by Quandles
  • Colorings of Knotted Surface Diagrams by Quandles
  
  
• Quandle Cocycle Invariants of Knots
  • Quandle -Cocycle Invariants of Classical Knots
  • Quandle -Cocycle Invariants of Classical Knots
  • Quandle -Cocycle Invariants of Knotted Surfaces
  • Polynomial Quandle Cocycles
  • Quandle Cocycle Invariants with Actions on Coefficients
  
  
• Applications of Cocycle Invariants
  • Extensions of Colorings
  • Chirality of knots and graphs
  • Colored chirality of knots
  • Minimal number of type III Reidemeister moves
  • Tangle embeddings
  • Non-invertibility of knotted surfaces
  • Minimal number of triple points on knotted surface projections
  • Minimal number of broken sheets in knotted surface diagrams
  • Ribbon concordance
  
  
• Bibliography
• About this document ...