Jones polynomial of a split union
= Jones polynomial of a split union
{c}
{title2=$V_{L\sqcup J}(t)=-(t^{1/2}+t^{-1/2})V_L(t)V_J(t)$}
Placing the two <link diagrams> in disjoint disks keeps all state <circles> separate. The reduced <Kauffman bracket> therefore acquires one extra loop factor $-A^2-A^{-2}$. Correcting <writhe of a link diagram> and setting $t=A^{-4}$ gives the displayed formula. It concerns a <split link>, not an arbitrary union of linked components.