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# Hyperbolic Structures on 3-manifolds, Ii: Surface Groups and 3-manifolds Which Fiber over the Circle

@inproceedings{Thurston2008HyperbolicSO, title={Hyperbolic Structures on 3-manifolds, Ii: Surface Groups and 3-manifolds Which Fiber over the Circle}, author={William P. Thurston}, year={2008} }

- Published 2008

The main result (0.1) of this paper is that every atoroidal three-manifold that fibers over the circle has a hyperbolic structure. Consequently, every fibered three-manifold admits a geometric decomposition. The main tool for constructing hyperbolic structures on fibered three-manifolds is the double limit theorem (4.1), which is of interest for its own sake and lays out general conditions under which sequences of quasi-Fuchsian groups have algebraically convergent subsequences. The main tool… CONTINUE READING

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