Let P be a finite complex on which _S_1 acts freely. In this paper, we shall give a sufficient condition that the kernel of the natural map (forgetful map) Aut_S_1 P → Aut P is a finite group.
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Hiroo Shiga, Toshihiro Yamaguchi, Principal Bundle Maps via Rational Homotopy Theory. Publ. Res. Inst. Math. Sci. 39 (2003), no. 1, pp. 49–57DOI 10.2977/PRIMS/1145476148