#### Volume 20, issue 1 (2016)

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Derived functors of the divided power functors

### Lawrence Breen, Roman Mikhailov and Antoine Touzé

Geometry & Topology 20 (2016) 257–352
##### Abstract

We study the derived functors of the components ${\Gamma }_{ℤ}^{d}\left(A\right)$ of the divided power algebra ${\Gamma }_{ℤ}\left(A\right)$ associated to an abelian group $A$, with special emphasis on the $d=4$ case. While our results have applications both to representation theory and to algebraic topology, we illustrate them here by providing a new functorial description of certain integral homology groups of the Eilenberg–Mac Lane spaces $K\left(A,n\right)$ for $A$ a free abelian group. In particular, we give a complete functorial description of the groups ${H}_{\ast }\left(K\left(A,3\right);ℤ\right)$ for such $A$.

##### Keywords
strict polynomial functors, derived functors of non-additive functors, Eilenberg–Mac Lane spaces
Primary: 18G55
Secondary: 55P20