Remark. Given n consider
the set of knots which have a diagram with n crossings but
not fewer crossings. Then for n = 3,4,5,6,7
colouring numbers distinguish the knots from each
other. But 82
and 83 have the same
colouring group Z17. In
the next section we will have an invariant which distinguishes these
two knots.
8_17
is achiral. A table of knots (up to 10 crossings) and their codes. Some diagrams drawn
from their codes. See what Tait had to say about 4.4 and Celtic knots.
Previous lecture
Next lecture