Fiberwise retraction and shape properties of the orbit space (Q2709918)
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scientific article
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Fiberwise retraction and shape properties of the orbit space |
scientific article |
Statements
3 July 2001
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equivariant retract
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equivariant fiberwise shape
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orbit space
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\(G\)-ANR
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\(G\)-shape
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\(G\)-resolution
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Fiberwise retraction and shape properties of the orbit space (English)
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The authors first study, from the point of view of retracts and shape theory, the category \(G\text{-TOP}_P\) of \(G\)-spaces over a \(G\)-space \(B\), where \(G\) is a compact group. In particular, they prove that if \(B\) has only one orbit type and \(E\) is a metric \(G\)-ANR over \(B\), then the orbit space \(E/G\) is an ANR over \(B/G\). As an application they construct a fiberwise \(G\)-orbit functor \(\mu:G\text{-}SH_B\to SH_{B/G}\) on shape level.
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