On equivariant fibrations of $G$-CW-complexes
Sbornik. Mathematics, Tome 210 (2019) no. 10, pp. 1428-1433
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It is proved that if $G$ is a compact Lie group, then an equivariant Serre fibration of $G$-CW-complexes is an equivariant Hurewicz fibration in the class of compactly generated $G$-spaces. In the nonequivariant setting, this result is due to Steinberger, West and Cauty. The main theorem is proved using the following key result: a $G$-CW-complex can be embedded as an equivariant retract in a simplicial $G$-complex. It is also proved that an equivariant map $p\colon E\to B$ of $G$-CW-complexes is a Hurewicz $G$-fibration if and only if the $H$-fixed point map $p^H\colon E^H \to B^H$ is a Hurewicz fibration for any closed subgroup $H$ of $G$. This gives a solution to the problem of James and Segal in the case of $G$-CW-complexes.
Bibliography: 9 titles.
Keywords:
$G$-CW-complex, simplicial $G$-complex, equivariant fibration, $H$-fixed points.
@article{SM_2019_210_10_a3,
author = {P. S. Gevorgyan and R. Jimenez},
title = {On equivariant fibrations of $G${-CW-complexes}},
journal = {Sbornik. Mathematics},
pages = {1428--1433},
publisher = {mathdoc},
volume = {210},
number = {10},
year = {2019},
language = {en},
url = {http://geodesic.mathdoc.fr/item/SM_2019_210_10_a3/}
}
P. S. Gevorgyan; R. Jimenez. On equivariant fibrations of $G$-CW-complexes. Sbornik. Mathematics, Tome 210 (2019) no. 10, pp. 1428-1433. http://geodesic.mathdoc.fr/item/SM_2019_210_10_a3/