Milnor-Lê type fibrations for subanalytic maps

Abstract

We prove a Milnor-Lê type fibration theorem for a subanalytic map $f:X\to Y$ between subanalytic sets $X\subset {\mathbb{R}}^m$ and $Y\subset {\mathbb{R}}^n$. Moreover, if $f$ extends to an analytic map ${\mathbb{R}}^m\to {\mathbb{R}}^n$, we define the singular set and the discriminant set of $f$, in a stratified sense. Then we give Milnor-Lê type fibration theorems for $f$ outside its discriminant, as well as over it. We give examples of each situation approached in this paper.

13 pages