Link}}(M_1\cap K_2,K_3)$ is denoted by ${\mbox{\rm Tlk}}_3(K_1,K_2,K_3)$.

-   Let $M_i$ be a Seifert hypersurface for $K_i$ $(i=1,3)$ such that $M_1\cap M_3$ is a $2$-manifold which intersects $K_2$ transversely. Count the intersections between them algebraically and denote the sum by ${\mbox{\rm Tlk}}_4(K_1,K_2,K_3)$.

-   Let $M_i$ be a Seifert hypersurface for $K_i$ $(i=1,2,3)$ and let $N_2$ be a regular neighbourhood of $K_2$ in ${\bf R}^4$. We may assume that $M_i\cap \partial N_2$ is a $2$-manifold in $\partial N_2$ and that $M_1\cap \partial N_2$, $M_2\cap \partial N_2$ and $M_3\cap \partial N_2$ intersect transversely in a finite number of points. Count the intersections algebraically and denote the sum by ${\mbox{\rm Tlk}}_5(K_1,K_2,K_3)$.

-   Let $f:F_1 \cup F_2 \cup F_3 \rightarrow {\bf R}^4$ denote an embedding of the disjoint union of oriented surfaces $F_i$ representing $F=K_1\cup K_2\cup K_3$. Define a map $L:F_1 \times F_2 \times F_3 \rightarrow S^3 \times S^3$ by $$L(x_1,x_2,x_3) = \left( \frac {f(x_1)-f(x_2)}{||f(x_1)-f(x_2)||},
    \frac {f(x_2)-f(x_3)}{||f(x_2)-f(x_3)||} \right)$$ for $x_1\in F_1$, $x_2\in F_2$ and $x_3 \in F_3$, and denote the degree of $L$ by ${\mbox{\rm Tlk}}_6(K_1,K_2,K_3)$.

${\mbox{\rm Tlk}}_i(K_1,K_2,K_3)=\pm{\mbox{\rm Tlk}}_j(K_1,K_2,K_3)$ for any $i,j=1,\dots,6.$

[**Remark.**]{} In general, the [*triple linking number*]{} ${\mbox{\rm Tlk}}(K_i,K_j,K_k)$ for $i\ne j\ne k$ is defined to be the sum of the signs of 