Let $M$ be a closed, orientable 3-manifold with a non-trivial differentiable $S^1$-action.


What does this imply for $M$? What are examples except for (products of) spheres?



$S^1$-action in three dimensions
You will find the complete answer in the papers


[Frank Raymond, Classification of the actions of the circle on 3-manifolds. Trans. Amer. Math. Soc. 131 1968 51–78.](http://www.ams.org/mathscinet-getitem?mr=219086) 


and


[Peter Orlik and Frank Raymond, Actions of SO(2) on 3-manifolds. 1968 Proc. Conf. on Transformation Groups (New Orleans, La., 1967) pp. 297–318 Springer, New York](http://www.ams.org/mathscinet-getitem?mr=263112) 


