# Milnor map

From Diffgeom

## Definition

Let be a complex polynomial in variables. can be viewed as a map . Let denote the zero set of . Then, on the complement of , we can define a map from to .

The **Milnor map** of at radius is the restriction of this map to the sphere of radius , centered at the origin, to .

# Facts=

By the Milnor fibration theorem, the Milnor map is a fibration whenever the origin is an isolated singular point of . Under such circumstances, it is termed the Milnor fibration.