Transfers generate the equivariant stable homotopy category
type: Item
instance of: scholarly article
title: Transfers generate the equivariant stable homotopy category
zbMATH Open document ID: 0830.55011
DOI: 10.1016/0166-8641(94)90131-7
author: Carlos Prieto
published in: Topology and its Applications
publication date: 1996-02-06T00:00:00Z
review text: B. Schäffer, in his thesis, essentially showed that the category of topological spaces and maps, in which Dold's fixed point transfers are added as morphisms, becomes equivalent to the stable homotopy category. In this work, the author establishes the analogous result for a suitable category of \(G\)-spaces, where \(G\) is a compact Lie group. This means that any stable map \(\alpha: X\to Y\) which is \(G\)-equivariant must factor as \(\varphi \circ \tau\) where \(\varphi\) comes from a continuous \(G\)- invariant map and \(\tau\) is a transfer arising from some \(G\)-fixed point situation.
Mathematics Subject Classification ID: 55R12
Mathematics Subject Classification ID: 55M20
Mathematics Subject Classification ID: 55N91
Mathematics Subject Classification ID: 55M25
Mathematics Subject Classification ID: 19L47
Mathematics Subject Classification ID: 55N15
Mathematics Subject Classification ID: 55P42
Mathematics Subject Classification ID: 55P91
Mathematics Subject Classification ID: 55Q91
zbMATH DE Number: 612398
zbMATH Keywords: equivariant fixed point theory
zbMATH Keywords: equivariant cohomology
zbMATH Keywords: Dold's fixed point transfers
zbMATH Keywords: compact Lie group
reviewed by: Daniel H. Gottlieb
MaRDI profile type: Publication
full work available at URL: 0166-8641(94)90131-7
OpenAlex ID: W1966211486
cites work: The fixed point transfer of fiber-preserving maps
cites work: Coincidence index for fiber-preserving maps: An approach to stable cohomotopy
cites work: Q3784849
cites work: Equivariant Fixed Point Index and Fixed Point Transfer in Nonzero Dimensions
cites work: Fixed point theory of parametrized equivariant maps
description: scientific article; zbMATH DE number 612398