Notes for AKT-090915/0:03:24

Review and additions to last class, corrections:

1. The Jones polynomial is usually normalized by diving by [math]\displaystyle{ \left\langle \bigcirc \right\rangle }[/math], the bracket of the unknot (i.e. dividing by an additional factor of [math]\displaystyle{ d }[/math]).
2. We can prove that for any knot [math]\displaystyle{ K }[/math], [math]\displaystyle{ J(K) }[/math] is a polynomial of [math]\displaystyle{ A^4 }[/math]. Hence, we can substitute [math]\displaystyle{ A=q^{1/4} }[/math] to get a Laurent polynomial in [math]\displaystyle{ q }[/math].