Notes for AKT-090917-1/0:46:11

Let [math]\displaystyle{ K }[/math] be a knot, [math]\displaystyle{ J_K(q) }[/math] be its Jones polynomial. Substitute [math]\displaystyle{ q = e^x }[/math] and expand [math]\displaystyle{ J_k(e^x) }[/math] into power series. We have [math]\displaystyle{ J_K(e^x) = \sum_n j_{(n,K)} \ x^n }[/math] where the coefficients [math]\displaystyle{ j_{(n,\cdot)}: \{knots \} \rightarrow \mathbb{Z} }[/math] are knot invariants.

Thm: [math]\displaystyle{ j_{(n, \cdot)} }[/math] is of type [math]\displaystyle{ n }[/math].