A characterization of equivariant absolute extensors and the equivariant Dugundji theorem
Let G be a compact Lie group. We prove that a metrizable G-space X is a G-ANE (resp., a G-AE) iff X is an ANE (resp., an AE) and, for any closed subgroup H C G, the H-fixed point set X[H] is a strong neighborhood H-deformation retract (resp., a strong H-deformation retract) of X. If a G-space X has...
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2005 |
| País: | México |
| Institución: | Universidad Nacional Autónoma de México |
| Repositorio: | Sistema de Información de la Facultad de Ciencias, UNAM |
| OAI Identifier: | oai:repositorio.fciencias.unam.mx:11154/1392 |
| Acceso en línea: | http://hdl.handle.net/11154/1392 |
| Access Level: | acceso abierto |
| Palabra clave: | Mathematics G-ANE equivariant extension, slice, H-fixed point set, H-orbit space |
| Sumario: | Let G be a compact Lie group. We prove that a metrizable G-space X is a G-ANE (resp., a G-AE) iff X is an ANE (resp., an AE) and, for any closed subgroup H C G, the H-fixed point set X[H] is a strong neighborhood H-deformation retract (resp., a strong H-deformation retract) of X. If a G-space X has no G-fixed point, then X is a G-ANE provided that X is an H-ANE for any subgroup H C G that occurs as a stabilizer in X. As an application, we give a new proof of the equivariant Dugundji extension theorem in the metrizable case. |
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