Representations of the Homology of BV and the Steenrod Algebra II

Abstract

Let V be an elementary Abelian 2-group of rank n, which it will usually be more useful to consider as an n-dimensional vector space over ${\Bbb F}$ ₂, the field with 2 elements. We write H*(V) and H _*(V) for the cohomology and homology of BV with ${\Bbb F}$ ₂-coefficients. Of course, BV is homotopy equivalent to the cartesian product of n copies of ℝP ^∞. The importance of H*(V) as a module or algebra over the mod 2 Steenrod algebra, A, in unstable homotopy is now well established. It is therefore to be expected that H*(V) itself has much inner subtlety.