Self homotopy equivalences of Stiefel manifolds \(W_{n,2}\) and \(V_{n,2}\) (Q791195)
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scientific article; zbMATH DE number 3850087
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Self homotopy equivalences of Stiefel manifolds \(W_{n,2}\) and \(V_{n,2}\) |
scientific article; zbMATH DE number 3850087 |
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Self homotopy equivalences of Stiefel manifolds \(W_{n,2}\) and \(V_{n,2}\) (English)
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1983
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The group \({\mathcal E}(X)\) of self-homotopy equivalence classes of a space X is already known in case X is an h-space which is also a complex with three cells. Here calculations are given for the real and complex Stiefel manifolds \[ V_{n,2}=O(n)/O(n-2)=S^{n-2}\cup e^{n-1}\cup e^{2n- 3}\quad(n\geq 6,\quad n\neq 8), \] \[ W_{n,2}=U(n)/U(n-2)=S^{2n-3}\cup e^{2n-1}\cup e^{4n-4}\quad(n\geq 5) \] both of which are sphere bundles over spheres. The calculations involve a secondary homotopy operation.
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groups of homotopy equivalence classes
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real and complex Stiefel manifolds
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sphere bundles over spheres
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secondary homotopy operation
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