Splittings of Surfaces

DOI10.1090/S0894-0347-96-00205-6zbMath0877.57002MaRDI QIDQ4874247

Richard K. Skora

Publication date: 11 June 1996

Published in: Journal of the American Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

fundamental grouphyperbolic surface\(R\)-treesgeodesic laminationtrain tracks

Mathematics Subject Classification ID

Geometric group theory (20F65) Ideal boundary theory for Riemann surfaces (30F25) Discrete subgroups of Lie groups (22E40) General geometric structures on low-dimensional manifolds (57M50) Fundamental group, presentations, free differential calculus (57M05) Teichmüller theory for Riemann surfaces (30F60) Foliations in differential topology; geometric theory (57R30)

Related Items

Holonomy limits of complex projective structures, Convergence of freely decomposable Kleinian groups, Combination Theorems in Groups, Geometry and Dynamics, Harmonic maps from surfaces to \(\mathbb{R}\)-trees, ℝ-trees, dual laminations and compact systems of partial isometries, Heegaard splittings and pseudo-Anosov maps, Non-realizability and ending laminations: proof of the density conjecture, High-energy harmonic maps and degeneration of minimal surfaces, Hitchin representations of Fuchsian groups, Connectivity of the Gromov boundary of the free factor complex, Local topology in deformation spaces of hyperbolic 3-manifolds, Connected components of the compactification of representation spaces of surface groups, On indecomposable trees in the boundary of outer space., Sur les automorphismes extérieurs des groupes hyperboliques, On the Morgan-Shalen compactification of the \(SL(2,\mathbb{C})\) character varieties of surface groups, Meromorphic quadratic differentials and measured foliations on a Riemann surface, Geometric compactification of moduli spaces of half-translation structures on surfaces, Realising end invariants by limits of minimally parabolic, geometrically finite groups, The Double Limit Theorem and Its Legacy, Automorphisms of character varieties, Constructing geometrically infinite groups on boundaries of deformation spaces, A compactification of outer space which is an absolute retract

Cites Work

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• Geometric actions of surface groups on \(\Lambda\)-trees
• Free actions of surface groups on \({\mathbb{R}}\)-trees
• Dendrology of groups in low \({\mathbb{Q}}\)-ranks
• Valuations, trees, and degenerations of hyperbolic structures. I
• Group actions on trees and the compactification of the space of classes of SO(n,1)-representations
• Degenerations of hyperbolic structures. III: Actions of 3-manifold groups on trees and Thurston's compactness theorem
• Measured lamination spaces for surfaces, from the topological viewpoint
• Hyperbolic structures on 3-manifolds. I: Deformation of acylindrical manifolds
• Ergodic theory and free actions of groups on \({\mathbb{R}}\)-trees
• Simplicial approximation and low-rank trees
• Foliations with measure preserving holonomy
• Relative growth rates of closed geodesics on a surface under varying hyperbolic structures
• Splittings of surfaces
• Group Actions On R-Trees
• Combinatorics of Train Tracks. (AM-125)
• Groups acting freely on R-trees