Twisted Homology of Configuration Spaces and Homology of Spaces of Equivariant Maps

Abstract

We calculate homology groups with certain twisted coefficients of configuration spaces of projective spaces. This completes a calculation of rational homology groups of spaces of odd maps of spheres S^m → S^M, m < M, and of the stable homology of spaces of non-resultant polynomial maps ℝ^m+1 → ℝ^M+1. Also, we calculate the homology of spaces of ℤ_r-equivariant maps of odd-dimensional spheres, and discuss further generalizations.