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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.
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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