Talk:Circle actions on 3-manifolds (Ex)
From Manifold Atlas
Insight: Try to quotient the manifold by the action. Note that you get something that looks kind of reasonable but isn't a manifold.
Guess: The isotropy groups must all be the same. Consider a point, then the isotropy groups of its neighborhood are the same as the point's. Consider the same method for a point on the boundary of an (open) region of fixed isotropy groups; this shows the set with identical isotropy groups is both open and closed. Then, the isotropy groups must in fact be . Then turn the action into one with trivial isotropy groups. Now take a quotient and use the lemma on Slide 14 of http://www.him.uni-bonn.de/lueck/data/Melbourne_I_Introduction_to_3-manifolds190107.pdf.