Exotic structures on quotient spaces of \(S^ 3\)-actions (Q1922869)

The present note is a result of our interest in finding exotic structures on 7-dimensional manifolds [cf. \textit{M. Guest} and the second author, Mathematika 41, 145-148 (1994; Zbl 0822.57023); the authors, Diffeomorphism type of Eschenburg spaces, Differ. Geom. Appl. (to appear)] and its purpose is to correct some mistakes that occur in a paper by \textit{A. Rigas} [Bull. Soc. Math. Fr. 112, 69-92 (1984; Zbl 0573.57010)]. Our contribution is simply to provide the correct statement and a different proof of the key corollary that appears on page 76 of Rigas [loc. cit.], but we take the opportunity to restate several results of the paper which refer to the existence of free \(S^3\) actions on \(S^7\times S^3\) and on the symplectic group \(Sp_2\) with quotients exotic seven-spheres, which also appear incorrectly stated in that paper.