is [*of type $(i,j)$*]{} if the upper decker curve lies in $K_i$ and the lower decker curve lies in $K_j$. A decker curve over $C^*$ is [*of type $(i,j)$*]{} if $C^*$ is so.

At a triple point $\tau$, if the orientation normals to the top, middle, and bottom sheets at $\tau$ matches with this order the fixed orientation of ${\bf R}^3$, then the sign of $\tau$ is positive and $\varepsilon(\tau)=+1$; otherwise the sign is negative and $\varepsilon(\tau)=-1$.

We interprete the triple linking ${\mbox{\rm Tlk}}_1$ in terms of double decker curves as follows. Let $D_{12}^{\ell}$ (resp. $D_{23}^u$) denote the union of lower decker curves of type $(1,2)$ (resp. upper decker curves of type $(2,3)$). Note that both $D_{12}^{\ell}$ and $D_{23}^u$ are contained in $K_2$.

${\mbox{\rm Tlk}}_1(K_1,K_2,K_3)=-{\mbox{\rm Int}}_{K_2}(D_{12}^{\ell},D_{23}^u),
$ where ${\mbox{\rm Int}}_{K_2}(D_{12}^{\ell},D_{23}^u)$ is the intersection number in $K_2$.

[*Proof.*]{} Let $\tau$ be a triple point of type $(1,2,3)$. The preimage of $\tau$ consists of three points of $F$. Exactly one of them is on $K_2$ and that is a double point of $D_{12}^{\ell}$ and $D_{23}^u$. Conversely the image of a double point of $D_{12}^{\ell}$ and $D_{23}^u$ is a triple point of $F^*$ of type $(1,2,3)$. Hence there is a one-to-one correspondence between 