On the equivariant homotopy of free abelian groups on \(G\)-spaces and \(G\)-spectra
type: Item
instance of: scholarly article
title: On the equivariant homotopy of free abelian groups on \(G\)-spaces and \(G\)-spectra
zbMATH Open document ID: 0882.55008
DOI: 10.1007/PL00004297
published in: Mathematische Zeitschrift
publication date: 1997-07-03T00:00:00Z
review text: 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 \(G\).
Mathematics Subject Classification ID: 55P42
Mathematics Subject Classification ID: 55P91
zbMATH DE Number: 1028167
zbMATH Keywords: Dold-Thom theorem
author: Paulo Lima-Filho
reviewed by: Victor P. Snaith
MaRDI profile type: Publication
full work available at URL: pl00004297
OpenAlex ID: W1978871002
description: scientific article; zbMATH DE number 1028167