A characterization of G-ANR and G-AR spaces for proper actions of Lie groups

Let G be a matrix Lie group. We prove that a proper G-space X of finite structure, which is metrizable by a G-invariant metric, is a G-ANR (resp., a G-AR) iff for any compact subgroup H⊂G the H-fixed point set XH is an ANR (resp., an AR). An equivariant embedding result for proper G-spaces of finite...

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Bibliographic Details
Published in:Topology and its applications 2017-11, Vol.231, p.292-305
Main Authors: Antonyan, Natella, Antonyan, Sergey A., Mata-Romero, Armando, Vargas-Betancourt, Enrique
Format: Article
Language:English
Subjects:
Equivariant extension
G-ANR
H-fixed point set
Lie group
Proper action
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Summary:Let G be a matrix Lie group. We prove that a proper G-space X of finite structure, which is metrizable by a G-invariant metric, is a G-ANR (resp., a G-AR) iff for any compact subgroup H⊂G the H-fixed point set XH is an ANR (resp., an AR). An equivariant embedding result for proper G-spaces of finite structure is also obtained.
ISSN:0166-8641
1879-3207
DOI:10.1016/j.topol.2017.09.018