On the equivariant homotopy of free abelian groups on \(G\)-spaces and \(G\)-spectra
In [\textit{A. Dold} and \textit{R. Thom}, Ann. Math., II. Ser. 67, 239-281 (1958; Zbl 0091.37102)] it is shown that the infinite symmetric product (or free abelian group) on a space \(X\) is a generalized Eilenberg-MacLane space \(K(H_* (X;\mathbb{Z}))\). If \(G\) is a finite group acting on \(X\), the author studies the Mackey functor given by the infinite symmetric product. In the unstable category this is shown to give a ``generalized Eilenberg-MacLane'' space associated to Bredon cohomology of \(X\) with coefficients in the constant Mackey functor, \(\mathbb{Z}\). A similar construction on \(G\)-spectra in the stable homotopy setting is shown to define a \(G\)-spectrum, \(\mathbb{Z}(E)\), so that \(\mathbb{Z}(S^0) =K(A(G),0)\), \(A(G)\) being the Burnside ring of \(G\).
scientific article; zbMATH DE number 1028167