Topology of complements of discriminants and resultants

Abstract

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