Configuration spaces and rational functions

In order to study the homology of the configuration space of unordered k-tuples of distinct points in ℂ, Arnold defined a space P_k,n ^l and performed an induction. Here P_k,n ^l is defined to be the space consisting of all monic polynomials f(z) over ℂ of degree k and such that the number of n-fold roots of f(z) is at most l. In this talk, we give a description of the stable homotopy type of P_k,n ^l by relating P_k,n ^l to a space consisting of certain n-tuples of monic polynomials.