CaTherine wheels unify structures across fields by providing a canonical bijection between orbit-equivalence classes of pseudo-Anosov flows without perfect fits, G-equivariant CaTherine wheels, minimal G-zippers, and connected components of uniform quasimorphisms for the fundamental group of any闭ed
Hyperbolic Structures on 3-manifolds, II: Surface groups and 3-manifolds which fiber over the circle
3 Pith papers cite this work. Polarity classification is still indexing.
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abstract
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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2026 3verdicts
UNVERDICTED 3representative citing papers
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.
An overview of the geometrisation theorem for 3-manifolds that explains its content and effects in various situations.
citing papers explorer
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CaTherine wheels
CaTherine wheels unify structures across fields by providing a canonical bijection between orbit-equivalence classes of pseudo-Anosov flows without perfect fits, G-equivariant CaTherine wheels, minimal G-zippers, and connected components of uniform quasimorphisms for the fundamental group of any闭ed
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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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Geometrisation of 3-manifolds
An overview of the geometrisation theorem for 3-manifolds that explains its content and effects in various situations.