Topology of complements of discriminants and resultants

In this paper, we classify the homotopy types of spaces of monic polynomial s which have no n-fold real roots or spaces of n-tuples of monic polynomial s which have no common real roots, by using the "scanning method" ([9]) and Vassiliev's spectral sequence ([15], [16]). In particular, we show that su ch spaces are finite dimensional models for the infinite dimensional loop s pace of spheres.