Canonical splittings of groups and 3-manifolds

DOI10.1090/S0002-9947-01-02871-9zbMath0981.57002arXivmath/0107232OpenAlexW1616942760MaRDI QIDQ2750931

G. P. Scott, Gadde A. Swarup

Publication date: 21 October 2001

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

Full work available at URL: https://arxiv.org/abs/math/0107232

zbMATH Keywords

3-manifoldends of groupsJSJ decompositioncharacteristic submanifoldDeformation Theorem

Mathematics Subject Classification ID

Topological methods in group theory (57M07) Free products of groups, free products with amalgamation, Higman-Neumann-Neumann extensions, and generalizations (20E06)

Related Items

Topological Equisingularity: Old Problems from a New Perspective (with an Appendix by G.-M. Greuel and G. Pfister on SINGULAR) ⋮ Regular neighbourhoods and canonical decompositions for groups ⋮ Splittings of groups and intersection numbers

Cites Work

• Unnamed Item
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• Finite group actions on 3-manifolds
• PL minimal surfaces in 3-manifolds
• Cyclic splittings of finitely presented groups and the canonical JSJ deccomposition
• Existence of incompressible minimal surfaces and the topology of three dimensional manifolds with non-negative scalar curvature
• Least area incompressible surfaces in 3-manifolds
• The classical Plateau problem and the topology of three-dimensional manifolds. The embedding of the solution given by Douglas-Morrey and an analytic proof of Dehn's lemma
• Homotopy equivalences of 3-manifolds with boundaries
• Cut points and canonical splittings of hyperbolic groups
• JSJ-splittings for finitely presented groups over slender groups
• Structure and rigidity in (Gromov) hyperbolic groups and discrete groups in rank \(1\) Lie groups. II
• Canonical decompositions of 3-manifolds
• The symmetry of intersection numbers in group theory
• Splittings of groups and intersection numbers
• A geometric characteristic splitting in all dimensions
• On free boundary Plateau problem for general dimensional surfaces
• JSJ-decompositions of finitely presented groups and complexes of groups.
• Eine Verallgemeinerung des Schleifensatzes
• Boundary respecting maps of 3-manifolds
• Boundary-reducible 3-manifolds and Waldhausen's theorem
• STRONG ANNULUS AND TORUS THEOREMS AND THE ENCLOSING PROPERTY OF CHARACTERISTIC SUBMANIFOLDS OF 3-MANIFOLDS
• A New Proof of the Annulus and Torus Theorems
• Boundary Preserving Maps of 3-Manifolds
• PL Involutions of Fibered 3-Manifolds
• On a Theorem of Johannson
• On $P^2$-irreducible 3-manifolds
• ON SUFFICIENTLY LARGE 3-MANIFOLDS