title: Immersion invariants in complex singularity theory

abstract:
A finitely determined holomorphic germ from C^2 to C^3 induces a
stable immersion from S^3 to S^5 on the level of links of space germs.
Its immersion invariants and some analytic invariants of the germ
determine each other. Namely, the number of Whitney umbrella points of
a holomorphic stabilization is equal to the Smale invariant of the
immersion (up to sign), which classifies the immersions up to regular
homotopy. Ekholm introduced an invariant of stable immersions, which
changes if and only if a regular homotopy steps through an immersion
with triple point. The Ekholm invariant can be expressed as a linear
combination of the number of Whitney umbrellas and the triple points
of a holomorphic stabilization.