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Hyperbolic Structures on 3-manifolds, II: Surface groups and 3-manifolds which fiber over the circle
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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).
Forward citations
Cited by 7 Pith papers
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On the Dirac complement problem
A new cohomology class obstructs the existence of Dirac complements, and for Lie algebras carrying a definite invariant pairing, the diagonal in g⊕ḡ admits a Dirac complement exactly when g is abelian — covering all r...
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Combinations and chromatography of paths of Kleinian groups
A new combination theorem for Chabauty paths yields a continuous path through Kleinian groups whose groups are pairwise non-isomorphic, and a decomposition theorem (chromatography) splits convex cocompact paths into f...
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Monodromies of surfaces in 3-manifolds, right-veeringness, and primeness of links
Alternative link diagrams are visually prime: a non-prime link with an alternative diagram always has a visible decomposition circle, subsuming previous results for alternating, positive, and homogeneous braid links.
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Correspondences on hyperelliptic surfaces, combination theorems, and Hurwitz spaces
A construction mates finitely many Fuchsian groups with finitely many Blaschke products on higher-genus hyperelliptic Riemann surfaces, and embeds the parameter space into Hurwitz spaces.
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Mostow rigidity for skew solenoidal manifolds
Proves Mostow rigidity for foliated bundles over closed hyperbolic manifolds (dim >=3) with completely invariant full-support measures, including solenoidal and skew-solenoidal cases via cocycles.
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Algebraic correspondences and Schwarz reflections: Where rational dynamics meets Kleinian groups
Algebraic correspondences mate rational maps with Kleinian groups, and the modular Mandelbrot set is homeomorphic to the Mandelbrot set—this survey reports those results.
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Geometrisation of 3-manifolds
An overview of the geometrisation theorem for 3-manifolds that explains its content and effects in various situations.
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