TITLE: Which surfaces have nontrivial actions of the circle (by homeomorphisms)?
QUESTION [9 upvotes]: Let $S$ be a $2$-dimensional manifold such that the circle $S^1$ acts nontrivially on $S$ by homeomorphisms.  What can we conclude about $S$?
If $S$ is a compact oriented surface on which $S^1$ acts nontrivially by diffeomorphisms, then I know how to prove that $S$ is either the sphere or a torus.  Probably this can be easily extended to non-oriented surfaces or to surfaces of finite type (i.e. compact surfaces minus a finite set of points).  But I don't know how to do this for either infinite-type surfaces, or for actions by homeomorphisms (and this seems fundamental since without some kind of differentiability I don't know how to show that the action preserves a Riemannian metric, which is the first step in the proof for diffeomorphisms).
I don't even know how to deal with actions by homeomorphisms on closed oriented surfaces, and this is what I am primarily interested in.  But I am interested in the more general question as well.

REPLY [4 votes]: The relevant reference is a paper of Borel:
Theorem(Borel): Let $M$ be compact hyperbolic manifold. Then every continuous circle action on $M$ is trivial.
A. Borel: On periodic maps of certain K(π, 1), In: Œuvres: Collected Papers III,
57-60. Springer, 1983.