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The motivation for this paper derives from the work of F. Cohen, R. Cohen, B. Mann and R. Milgram ([5], [6]) and that of V. Vassiliev ([15]). The former gives a description of the stable homotopy type of the space of basepoint preserving holomorphic maps of degree d from the Riemann sphere S = C ∪ ∞ to the complex projective space CP. We denote this space by Hold(S,CP). Let Dj = F (C, j)+∧Σj S be the j-th subquotient of the May-Milgram model for ΩS ([11], [14]), where F (X, j) denotes the configuration space of j disjoint points in X,

Stable splitting of the space of polynomials with roots of bounded multiplicity