On the Topology of Polynomial Hypersurfaces
It is shown that for a large class of polynomials (tame polynomials), F: Cn -> C, the smooth level sets F-1 (a) have the homotopy type of a bouquet of spheres of dimension n , where µ, is the total Milnor number of F. A siimilar result under slightlv different hypotheses has been reported by Kouchnirenko. The result is deduced from the Milnor Fibration Theorem using standard homology and homotopy arguments.
Broughton, S.A. (1983). On the topology of polynomial hypersurfaces. In Proceedings of the Symposia Pure Mathematics, 40, 167-178.