In the paper ["A survey of group actions on 4-manifolds" by
Allan L. Edmonds](https://arxiv.org/pdf/0907.0454.pdf) on page 5 there is the remark "One should note that the coned-off E8-plumbing manifold
admits a circle action that does have more than four orbit types in a neighbourhood of the
cone point."

I guess this answers [my previous question](https://mathoverflow.net/questions/403581/non-smooth-manifold-with-circle-action-with-fixed-points), but I am not sure since I guess it is possible that the fixed point set it not a submanifold (I only know how to prove this for smooth $S^1$-actions). Could somebody explain how this circle action is constructed? what is the fixed point set? is it a submanifold?