Robinson-Whitehouse complex and stable homotopy
type: Item
instance of: scholarly article
title: Robinson-Whitehouse complex and stable homotopy
zbMATH Open document ID: 0957.18005
DOI: 10.1016/S0040-9383(99)00014-2
author: Birgit Richter
author: Teimuraz Pirashvili
published in: Topology
publication date: 2000-04-26T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 18G60
Mathematics Subject Classification ID: 55P47
Mathematics Subject Classification ID: 13D03
zbMATH DE Number: 1436049
zbMATH Keywords: category of finite pointed sets
zbMATH Keywords: André's construction
zbMATH Keywords: homology groups
zbMATH Keywords: spectrum
reviewed by: Timothy Porter
MaRDI profile type: Publication
full work available at URL: s0040-9383(99)00014-2
OpenAlex ID: W2003867453
description: scientific article; zbMATH DE number 1436049