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\(S^ 3\)-bundles and exotic actions. (English) Zbl 0573.57010
Explicit representatives for all principal bundles with group \(S^ 3\) and SO(4) over \(S^ 4\) and \(S^ 7\) are constructed and insight is gained into the free \(S^ 3\)-action on \(S^ 7\times S^ 3\) with quotient a seven-dimensional sphere with nonstandard differentiable structure.
Reviewer: H.Hösli

MSC:
57R22 Topology of vector bundles and fiber bundles
57S25 Groups acting on specific manifolds
57R60 Homotopy spheres, Poincaré conjecture
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