Equivariant Eilenberg-MacLane spaces K(\({\mathcal G},\mu,1)\) for possibly non-connected or empty fixed point sets
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)].
equivariant Eilenberg-MacLane spaces of type one
scientific article; zbMATH DE number 4001013