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Nov 1, 2020 at 15:18 comment added CuriousUser Thank you for the suggestions. I do not think that the action you mention can extend to an almost free circle action, though: even if a circle extension was possible, I would imagine that the point at infinity would be a fixed point for the whole circle. Also, I was aware of the survey you mention (very nice one), but again I see no mention of the problem I am interested in. Finally, I wonder if there are examples of cyclic group actions whose fixed point set has positive dimension but it is not a rational sphere.
Oct 31, 2020 at 19:22 history answered Nicholas Kuhn CC BY-SA 4.0