Linearization of proper group actions |
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Authors: | Natella Antonyan Leonardo Rodríguez-Medina |
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Institution: | a Departamento de Matemáticas, Division de Ingeniería y Arquitectura, Instituto Tecnológico y de Estudios Superiores de Monterrey, Campus Ciudad de México, 14380 México Distrito Federal, Mexico b Departamento de Matemáticas, Facultad de Ciencias, Universidad Nacional Autónoma de México, 04510 México Distrito Federal, Mexico |
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Abstract: | We prove that if G is a locally compact group acting properly (in the sense of R. Palais) on a space X that is metrizable by a G-invariant metric, then X can be embedded equivariantly into a normed linear G-space E endowed with a linear isometric G-action which is proper on the complement E?{0}. If, in addition, G is a Lie group then E?{0} is a G-equivariant absolute extensor. One can make this equivariant embedding even closed, but in this case the non-proper part of the linearizing G-space E may be an entire subspace instead of {0}. |
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Keywords: | 54C55 54C25 54H15 |
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