On the homology of spaces of equivariant maps

Abstract

A spectral sequence calculating the homology groups of some spaces of maps equivariant under compact group actions is described. For the main motivating example, we calculate the rational homology groups of spaces of even and odd maps [Formula: see text], [Formula: see text], or, which is the same, the stable homology groups of spaces of non-resultant homogeneous polynomial maps [Formula: see text] of increasing degree. Also, we calculate the homology groups of spaces of [Formula: see text]-equivariant maps of odd-dimensional spheres for any [Formula: see text]. In auxiliary calculations, we find the homology groups of configuration spaces of projective and lens spaces with coefficients in several local systems.