On self-maps which induce identity automorphisms of homology groups (Q2731113)
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scientific article; zbMATH DE number 1625558
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On self-maps which induce identity automorphisms of homology groups |
scientific article; zbMATH DE number 1625558 |
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On self-maps which induce identity automorphisms of homology groups (English)
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26 February 2002
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homotopy self equivalences
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\(P\)-localization
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0.9423783
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0.93727666
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0.91648835
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0.9133122
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0.88668036
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0.88558376
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Let \(X\) be a pointed CW-complex and let \(\Aut_*X\) be the group of homotopy classes of self-equivalences of \(X\) which induce identity on homology groups. The author proves that if \(X\) is countable, simply connected and finite-dimensional, then every element of \(\Aut_*X\) can be represented by a cellular map whose restriction to every skeleton \(X^q\) belongs to \(\Aut_*X^q\). The author also formulates some conditions for the triviality of \(\Aut_*X\).
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