Homotopy and homology of simplicial Abelian Hopf algebras
This paper takes as its starting point the fact that the mod \(p\) cohomology of the Eilenberg-MacLane space \(K(G,n)\) (\(G\) Abelian and \(n>0\)) depends only on \(\text{Tor}_0(\mathbb{Z}/p,G)\) and \(\text{Tor}_1(\mathbb{Z}/p,G)\). The authors generalize this and emphasize that it is essentially an algebraic, not a topological, fact. The main result is that the homotopy of a connected, simplicial, bicommutative Hopf algebra over \(\mathbb{F}_2\) is a functor of its André-Quillen homology. Since the traditional approach to computing this homology uses the homotopy as input, the authors give a new method for this computation, using Dieudonné theory.
scientific article; zbMATH DE number 1295397