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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Equivariant embedding of metrizable $ G$-spaces in linear $ G$-spaces


Author: Aasa Feragen
Journal: Proc. Amer. Math. Soc. 136 (2008), 2985-2995
MSC (2000): Primary 57S20
DOI: https://doi.org/10.1090/S0002-9939-08-09307-6
Published electronically: April 15, 2008
MathSciNet review: 2399067
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Abstract: Given a Lie group $ G$ we study the class $ \mathcal{M}_G$ of proper metrizable $ G$-spaces with metrizable orbit spaces, and show that any $ G$-space $ X \in \mathcal{M}_G$ admits a closed $ G$-embedding into a convex $ G$-subset $ C$ of some locally convex linear $ G$-space, such that $ X$ has some $ G$-neighborhood in $ C$ which belongs to the class $ \mathcal{M}_G$. As a corollary we see that any $ G$-ANR for $ \mathcal{M}_G$ is a $ G$-ANE for $ \mathcal{M}_G$.


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Additional Information

Aasa Feragen
Affiliation: Department of Mathematics, University of Helsinki, F-I-00014 Helsinki, Finland
Address at time of publication: Department of Mathematical Sciences, University of Aarhus, NY Munkegade, Building 1530, DK-8000 Aarhus, Denmark
Email: aasa.feragen@helsinki.fi

DOI: https://doi.org/10.1090/S0002-9939-08-09307-6
Keywords: Proper actions, tubular covering, equivariant embedding
Received by editor(s): August 7, 2006
Received by editor(s) in revised form: July 3, 2007
Published electronically: April 15, 2008
Additional Notes: The research leading to this article was financed by the Magnus Ehrnrooth Foundation.
Communicated by: Paul Goerss
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.