Knot Theory MA3F2                                         1                    

1. Identify the following knots. Use knot tables overleaf. String may help!



2. Find Reidemeister moves:     
                                              
3. Prove the following knot is achiral(isotopic  to its mirror image) and (harder) identify it in the knot tables.  
                                         
4. Find Reidemeister moves:
                                      
5. The following link occurs in an engraving by Durer. Find colouring and linking numbers.
What is the writhe of the link? What is the writhe after 12 R1 moves?
                                                          
6. Show that either one of the pair of R3 moves may be omitted. Show that R3 may be replaced by the detour move: 
  
7. Can colouring numbers distinguish: 41 from 51,  51 from 52, ....


Brian Sanderson.               Email:  bjs@maths.warwick.ac.uk
                                          Web:  http://www.maths.warwick.ac.uk/~bjs