I was looking up the Jones Polynomial for a project I’m working on and came up with this equation from the knot atlas:
$$ -q^3-q^{-3}+3q^2+3q^{-2}-2q-2q^{-1}+4 $$
However, I know that when entering VL(1), you should get the number of components required for the knot/link, and this equation churns out a 4 and not a 3 for a simple borromean.
Is this the actual Jones Polynomial? And if so, why does it produce this result? I’m simply an enthusiast and not a mathematician, so any explanation is beneficial.