Return to Revisions

There is an $S^1$-action on the Quaternionic projective plane $\mathbb{H}\mathbb{P}^2$ with exactly 3 fixed points. They are not hard to construct (done in a similar way to the standard $S^1$-actions on $\mathbb{C}\mathbb{P}^2$) the details of such an action are contained here https://arxiv.org/pdf/1401.4731.pdf. There Kustarev proves that any $S^1$-action on a oriented smooth $8$-manifold with three fixed points must have the same weights as some linear action on $\mathbb{H}\mathbb{P}^2$ and under mild hypothesis must be diffeomorphic to $\mathbb{H}\mathbb{P}^2$.