Hypersurface complements, Milnor fibers and higher homotopy groups of arrangements

The interplay between geometry and topology on complex algebraic varieties is a classical theme that goes back to Lefschetz. Our paper follows this line of investigation, for complements of homogeneous hypersurfaces and the corresponding global Milnor fibers. We use Morse theory to derive, in §§2-3, Theorems 1. and 3., two general results on CWstructures