Department of Mathematics
Hyperbolic Structures on 3-manifolds, II: Surface groups and 3-manifolds which fiber
over the circle
- Author(s): Thurston, William P.
- et al.
Published Web Locationhttps://arxiv.org/pdf/math/9801045.pdf
Geometrization theorem, fibered case: Every three-manifold that fibers over the circle admits a geometric decomposition. Double limit theorem: for any sequence of quasi-Fuchsian groups whose controlling pair of conformal structures tends toward a pair of projectively measured laminations that bind the surface, there is a convergent subsequence. This preprint also analyzes the quasi-isometric geometry of quasi-Fuchsian 3-manifolds. This eprint is based on a 1986 preprint, which was refereed and accepted for publication, but which I neglected to correct and return. The referee's corrections have now been incorporated, but it is largely the same as the 1986 version (which was a significant revision of a 1981 version).