Robinson-Whitehouse complex and stable homotopy
Let \(\Gamma\) be the small category of finite pointed sets, then for any \(\Gamma\)-module, i.e., functor \(F:\Gamma\to k\)-mod, the authors use a variant of André's construction to define homology groups \(H^\Gamma_*(F)\). This generalises a similar construction of \textit{S. Whitehouse}. Again using \(F\), one can extend it to all pointed sets using direct limits and degreewise to a functor from simplicial sets to simplicial modules. It is known that the homotopy of the spectrum corresponding to the \(\Gamma\)-space \(F\) is given by \(\pi_*^{ST}(F)= \text{colim} \pi_{*+n}F(S^n)\). This paper proves that \(\pi_*^{ST}(F)\) and \(H_*^\Gamma(F)\) are naturally isomorphic.
scientific article; zbMATH DE number 1436049