On an exotic fixed point-free smooth involution, hence a free smooth $\mathbb{Z}/2$-action on the 4-sphere:

- Ronald Fintushel, Ronald J. Stern,
*An Exotic Free Involution on $S^4$*, Annals of Mathematics Second Series, Vol. 113, No. 2 (Mar., 1981), pp. 357-365 (jstor:2006987)

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