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Correction for the paper “\(S^3\)-bundles and exotic actions” Bull. Soc. Math. France 112 (1984), 69-92. (English) Zbl 0993.57015
Summary: In [ibid. 112, 69-92 (1984; Zbl 0573.57010)], A. Rigas constructed explicit representatives for \(S^3\)-principal bundles over \(S^7\). Based on these constructions explicit free \(S^3\)-actions on the total spaces are described, with quotients exotic \(7\)-spheres. To describe these actions a classification formula for the bundles is used. This formula is not correct. We correct the classification formula and exhibit the correct indices of the exotic \(7\)-spheres that occur as quotients of the free \(S^3\)-actions described above.
MSC:
57R22 Topology of vector bundles and fiber bundles
55R25 Sphere bundles and vector bundles in algebraic topology
57R60 Homotopy spheres, Poincaré conjecture
57S25 Groups acting on specific manifolds
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