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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
##### Keywords:
principal bundles; exotic spheres; exotic actions
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