Hyperbolic Structures on 3-manifolds, II: Surface groups and 3-manifolds which fiber over the circle

Details Hyperbolic Structures on 3-manifolds, II: Surface groups and 3-manifolds which fiber over the circle Hyperbolic Structures on 3-manifolds, II: Surface groups and 3-manifolds which fiber over the circle

1998-01-10

arxiv.org/abs/math/9801045v1

Mathematics

Geometric Topology

32 pages, 6 figures, revision of 1986 preprint

Scientific paper

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).

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