K_2]_{E_3}$ in $H_1(E_3) \cong H_1(S^4 \backslash K_3)$. ) The case $k=3$ is reduced to the previous case ($k=1$) by use of Theorem 1.2(i).  

Proof of Proposition 1.6
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\(1) Let $\ell=k_1\cup k_2$ be a $(2,2a)$-torus link in a $3$-disk $D^3$ with ${\mbox{\rm Link}}(k_1,k_2)=a$. Let $\gamma$ be a simple loop in ${\bf R}^4$ which intersects a $3$-disk $B_0$ in ${\bf R}^4$ transversely at a single interior point of $B_0$ in the positive direction. Identify $D^3\times S^1$ with a regular neighborhood $N(\gamma)$ of $\gamma$ in ${\bf R}^4$ and let $T_1\cup T_2$ be the image of $\ell\times S^1=k_1\times S^1\cup k_2\times S^1$ in ${\bf R}^4$. Let $F=K_1\cup K_2\cup K_3$ be a surface-link with $K_1=T_1$, $K_2=T_2$ and $K_3=\partial B_0$. Then $F$ is the desired link.

\(2) Let $\ell= k_1 \cup k_2 \cup k_3$ be a pretzel link of type $(2a, -2b)$ in a 3-disk $D^3$ so that ${\mbox{\rm Link}}(k_1, k_2)=a$, ${\mbox{\rm Link}}(k_2, k_3)= -b$ and ${\mbox{\rm Link}}(k_1, k_3)=0$. Let $B_1, B_2, B_3$ be mutually disjoint 3-disks embedded in ${\bf R}^4$ and let $\gamma$ be a simple loop in ${\bf R}^4$ which intersects $B_i$ ($i=1,2,3$) transversely at a single interior point of $B_i$ in the positive direction. Identify $D^3 \times S^1$ with a regular neighborhood $N(\gamma)$ 