  We describe a new relation between the topology of hypersurface complements,
  Milnor fibers and degree of gradient mappings. The main tools are polar
curves and the affine Lefschetz theory developped by H. Hamm and A. N\'emethi.
  In the special case of the hyperplane arrangements, we strengthen some
results due to Orlik and Terao (see Math. Ann.
  301(1995)) and obtain an independant proof for the minimality of hyperplane
arrangements (see Randell math.AT/0011101 for another proof of this result).
