I am stucked, to show the following statement:
Let $L = L_1 \cup L_2$ be a split link. Show that $det(L)=0$ but $\sigma(L)= \sigma(L_1) + \sigma (L_2)$. Where $det$ means the determinant of the link and $\sigma$ his signature.
I know that I should observe the corresponding Seifert matrix of $L$ but I don't know how to do it. Any help would be appreciated!