Degenerations of hyperbolic structures. III: Actions of 3-manifold groups on trees and Thurston's compactness theorem

DOI10.2307/2007003zbMath0661.57004OpenAlexW2331921018MaRDI QIDQ1113138

John W. Morgan, Peter B. Shalen

Publication date: 1988

Published in: Annals of Mathematics. Second Series (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2307/2007003

zbMATH Keywords

measured laminationscharacteristic submanifoldmeasured laminations in 3-manifoldsaction on an \({\mathbb{R}}\)-treecompact, orientable, connected, irreducible 3-manifoldfaithful representations of the fundamental group into \(SL_ 2({\mathbb{C}})\)spaces of characters

Mathematics Subject Classification ID

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Structure and rigidity in hyperbolic groups. I ⋮ On the degeneration of Schottky groups. ⋮ Convergence of freely decomposable Kleinian groups ⋮ Algebraic Convergence of Schottky Groups ⋮ EXCEPTIONAL SEIFERT GROUP ACTIONS ON R ⋮ Infinitely many hyperbolic 3-manifolds which contain no Reebless foliation ⋮ Combination Theorems in Groups, Geometry and Dynamics ⋮ Skinning maps ⋮ Λ-trees and their applications ⋮ Geometry of pseudocharacters. ⋮ The Gromov topology on \({\mathbb{R}}\)-trees ⋮ Ergodic theory and free actions of groups on \({\mathbb{R}}\)-trees ⋮ ENDOMORPHISMS OF RELATIVELY HYPERBOLIC GROUPS ⋮ Skinning maps are finite-to-one ⋮ Circle Maps, Measured Laminations, and Free Group Actions on IR-trees ⋮ Groups acting on hyperbolic spaces -- a survey ⋮ Intellectual generosity and the reward structure of mathematics ⋮ Splittings of Surfaces ⋮ A sheaf-theoretic model for SL \((2, \mathbb C)\) Floer homology ⋮ Parametrization of PSL\((2,\mathbb C)\)-representations of surface groups ⋮ Independent generators for one-dimensional systems of isometries ⋮ The Poincaré metric and a conformal version of a theorem of Thurston ⋮ RECONSTRUCTING GROUP ACTIONS ⋮ ACTIONS, LENGTH FUNCTIONS, AND NON-ARCHIMEDEAN WORDS ⋮ Tropicalization of group representations ⋮ An effective compactness theorem for Coxeter groups. ⋮ Pleating of hyperbolic 3-manifolds ⋮ Divisible convex sets. IV: Boundary structure in dimension 3 ⋮ Group actions on order trees ⋮ Limits of geometrically tame Kleinian groups ⋮ Character varieties of higher dimensional representations and splittings of 3-manifolds ⋮ Bounded combinatorics and uniform models for hyperbolic 3-manifolds ⋮ Heegaard surfaces and measured laminations, II: Non-Haken 3–manifolds ⋮ A Glimpse into Thurston’s Work ⋮ A Survey of the Impact of Thurston’s Work on Knot Theory ⋮ The Double Limit Theorem and Its Legacy ⋮ On limits of quasi-conformal deformations of Kleinian groups ⋮ Codimension-1 simplices in divisible convex domains ⋮ Constructing geometrically infinite groups on boundaries of deformation spaces ⋮ Translation equivalence in free groups ⋮ Flats in 3-manifolds

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