  The image of a finitely determined holomorphic germ $\Phi$ from
$\mathbb{C}^2$ to $\mathbb{C}^3$ defines a hypersurface singularity $(X,0)$,
which is in general non-isolated. We show that the diffeomorphism type of the
boundary of the Milnor fibre $\partial F$ of $X$ is a topological invariant of
the germ $\Phi$. We establish a correspondence between the gluing coefficients
(so-called vertical indices) used in the construction of $\partial F$ and a
linking invariant $L$ of the associated sphere immersion introduced by T.
Ekholm and A. Sz\H{u}cs. For this we provide a direct proof of the equivalence
of the different definitions of $L$. Since $L$ can be expressed in terms of the
cross cap number $C(\Phi)$ and the triple point number $T(\Phi)$ of a stable
deformation of $\Phi$, we obtain a relation between these invariants and the
vertical indices. This is illustrated on several examples.
