Milnor Fibrations and the Thom Property for maps $f\bar{g}$

Abstract

We prove that every map-germ ${f \bar g}: (\C^n,\0) {\to}(\C,0)$ with an isolated critical value at 0 has the Thom $a_{f\bar{g}}$-property. This extends Hironaka's theorem for holomorphic mappings to the case of map-germs $f\bar{g}$ and it implies that every such map-germ has a Milnor-Lê fibration defined on a Milnor tube. One thus has a locally trivial fibration $ϕ: \mathbb S_\e \setminus K \to \mathbb S^1$ for every sufficiently small sphere around $\0$, where $K$ is the link of $f\bar{g}$ and in a neighbourhood of $K$ the projection map $\varphi$ is given by $f\bar{g}/|f\bar{g}|$.

6 pages