G-fibrant extensions and twisted products

Let G be a compact metrizable group and H its closed subgroup. We prove that every compact metrizable G-space over G/H admits a G-fibrant extension over G/H. This implies that the functor of twisted product G×H− takes H-fibrant extensions to G-fibrant extensions. In particular, the twisted product G...

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Bibliographic Details
Published inTopology and its applications Vol. 201; pp. 157 - 170
Main Authors Bykov, Alexander, Sánchez Martínez, Jorge Alberto
Format Journal Article
LanguageEnglish
Published Elsevier B.V 15.03.2016
Subjects
G-ANR
G-fibrant space
G-fibration
Orbit space
G-fibration
G-ANR
54C56
54C55
G-fibrant space
Orbit space
54H15
55R91
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Summary:Let G be a compact metrizable group and H its closed subgroup. We prove that every compact metrizable G-space over G/H admits a G-fibrant extension over G/H. This implies that the functor of twisted product G×H− takes H-fibrant extensions to G-fibrant extensions. In particular, the twisted product G×HS is a G-fibrant space when S is a compact H-fibrant space.
ISSN:0166-8641
1879-3207
DOI:10.1016/j.topol.2015.12.034