Almost connected groups as G-fibrant spaces

Abstract

The concept of G-SSDR-maps, as an equivariant version of SSDR-maps in the sense of F. Cathey, is defined for non compact groups actions. We prove that if G is a not necessarily compact Lie group or an almost connected metrizable group and N is its closed normal subgroup, the canonical projection GG/N is a strong G-fibration. As a consequence, it is shown that any almost connected metrizable group G is a G-fibrant space.