Equivariant Eilenberg-MacLane spaces K(\({\mathcal G},\mu,1)\) for possibly non-connected or empty fixed point sets
type: Item
instance of: scholarly article
title: Equivariant Eilenberg-MacLane spaces K(\({\mathcal G},\mu,1)\) for possibly non-connected or empty fixed point sets
zbMATH Open document ID: 0617.57021
DOI: 10.1007/BF01169083
author: Wolfgang Lück
published in: Manuscripta Mathematica
publication date: 1987-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/155211
review text: Equivariant Eilenberg-MacLane spaces were constructed by \textit{G. E. Bredon} [Equivariant cohomology theories (Lect. Notes Math. 34) (1967; Zbl 0162.272)], \textit{A. D. Elmendorf} [Trans. Am. Math. Soc. 277, 275- 284 (1983; Zbl 0521.57027)] and \textit{G. Triantafillou}, Bonn. Math. Schr. 110 (1978; Zbl 0429.55001)], however, only for nonempty connected H-fixed point sets for \(H\subset G\) and in the pointed category. This is a reasonable assumption in equivariant homotopy theory (equivariant Postnikov systems, homology, obstruction theory) but too restrictive for the study of equivariant manifolds. We develop a treatment of equivariant Eilenberg-MacLane spaces of type one in full generality. They are used, for example, in equivariant L- theory as reference spaces [see the author and \textit{I. Madsen}, ''Equivariant L-groups'', preprint, Aarhus (1987) or the author, Math. Gottingensis, Schriftenr. Sonderforschungsbereichs Geom. Anal. 69 (1986; Zbl 0605.57019)].
Mathematics Subject Classification ID: 57S10
Mathematics Subject Classification ID: 57S15
Mathematics Subject Classification ID: 57R67
Mathematics Subject Classification ID: 57R91
zbMATH DE Number: 4001013
zbMATH Keywords: equivariant Eilenberg-MacLane spaces of type one
zbMATH Keywords: equivariant L-theory
MaRDI profile type: Publication
cites work: Transformation groups
cites work: Systems of Fixed Point Sets
cites work: Q3742349
cites work: Classifying spaces and spectral sequences
cites work: Q3866798
description: scientific article; zbMATH DE number 4001013