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Oct 26, 2017 at 8:59 comment added HJRW By the way, you're right that the connection between representations of groups into $\mathrm{Homeo}(S^1)$ and 3-manifold topology is via circle bundles. Seifert-fibred 3-manifolds are a kind of generalization of circle bundles over surfaces.
Oct 26, 2017 at 8:57 comment added HJRW It sounds like what you want is broad background to the Calegari--Walker paper and related work. I recommend Calegari's two books: Foliations and the Geometry of 3-Manifolds and scl. Both can be downloaded in pdf format from his website: math.uchicago.edu/~dannyc .
Oct 25, 2017 at 23:20 history asked john mangual CC BY-SA 3.0