# $S^1$-action in three dimensions

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?

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The standard examples are Seifert fibre spaces, which admit a free $S^1$ action. The wikipedia page gives a reasonable description and some references. –  HJRW Oct 10 '11 at 18:26
@HW: they are standard examples, but not the only examples. In particular, if you allow fixed points, you get direct sums of lens spaces (proved in the Raymond paper, where a complete classification is given). –  Igor Rivin Oct 10 '11 at 19:32

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He will find the complete answer only if he finds the second paper, which is nontrivial. –  Igor Rivin Oct 10 '11 at 18:30
Only nontrivial if you don't know where to look :) –  José Figueroa-O'Farrill Oct 10 '11 at 19:19
Is interlibrary loan really nontrivial these days? –  Richard Kent Oct 10 '11 at 19:39
You don't know the OP's situation. He might be thinking these things in the jungles of amazon (though his web page indicates that he is in Bonn, and the book is, with high probability, in the MPI library, I admit). –  Igor Rivin Oct 10 '11 at 19:42
You've got me there. –  Richard Kent Oct 10 '11 at 20:12