On equivariant fibrations of -CW-complexes

Abstract

It is proved that if is a compact Lie group, then an equivariant Serre fibration of -CW-complexes is an equivariant Hurewicz fibration in the class of compactly generated -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 -CW-complex can be embedded as an equivariant retract in a simplicial -complex. It is also proved that an equivariant map of -CW-complexes is a Hurewicz -fibration if and only if the -fixed point map is a Hurewicz fibration for any closed subgroup of . This gives a solution to the problem of James and Segal in the case of -CW-complexes. Bibliography: 9 titles.