The Milnor number of a holomorphic function germ 
with an isolated critical
point is the complex dimension of its Jacobian
algebra,
 |
The denominator is the ideal generated by its partial derivatives. The nearby Milnor fiber has the homotopy
type of a bouquet of 
spheres of real dimension 
. For 
, the number is 1, while 
has Milnor number 
for integers 
.
The mu-constant problem asks whether keeping this number fixed in a family also keeps the defining function topologically unchanged. Constancy of multiplicity is a different assertion from this ambient topological triviality.
