A loop space whose homology has torsion of all orders (Q802168)
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scientific article; zbMATH DE number 3881481
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A loop space whose homology has torsion of all orders |
scientific article; zbMATH DE number 3881481 |
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A loop space whose homology has torsion of all orders (English)
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1986
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In this note a simply-connected finite CW complex X of dimension four is constructed with the following property. For each positive integer m, there is an element \(\omega_ m\) of order m in \(\pi_{m+1}(\Omega X)\) whose Hurewicz image \(h(\omega_ m)\in H_{m+1}(\Omega X)\) also has order m. Such a space illustrates how intricate loop space homology can be even for relatively simple spaces.
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graded algebras
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torsion in the homotopy groups of loop spaces
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torsion in the homology groups of loop spaces
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Hurewicz map
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