1. Identify the following knots. Use knot tables overleaf. String may
help!
2. Find Reidemeister moves:
![](images/ex1.2.jpg)
3. Prove the following knot is achiral(isotopic to its mirror
image) and (harder) identify it in the knot
tables.
![](images/ex1.3.jpg)
4. Find Reidemeister moves:
![](images/ex1.4.jpg)
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?
![](images/ex1.5.jpg)
6. Show that either one of the pair of R3 moves may be omitted. Show
that R3 may be replaced by the
detour
move:
![](images/ex1.6.jpg)
7. Can colouring numbers distinguish: 4
1 from 51,
51
from 52, ....
Brian
Sanderson.
Email: bjs@maths.warwick.ac.uk
Web: http://www.maths.warwick.ac.uk/~bjs