Resolutions of cohomology algebras and other struggles with integer coefficients

Abstract

There is a well known homotopy Π-algebra resolution of a space by wedges of spheres. An attempt to construct the Eckmann-Hilton dual gives a nice resolution for Fp coefficients which can then be used in a spectral sequence. For ℤ coefficients the dual construction has several compounding problems illustrating that integral cohomology becomes relatively problematic when we try to include primary operations.