This question is closely related to another I asked today.
Giffen showed in 1966 that the generalized Smith conjecture is false by constructing for odd $p$ a smooth $Z_p$ action on $S^4$ with fixed-point set a knotted $S^2$.
Is there a topological description of the quotient?
D. W. Sumners in 1975 extended Giffen's work by giving a different construction which also worked for $p$ even. I would be equally happy with a description of this quotient. More generally, I would be satisfied with a topological description of the quotient of any four-sphere by any smooth cyclic action that fixes a knotted two-sphere.
