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.

Keywords

• primary cohomology operations
• integer coefficients
• free resolution
• derived functors