Strong accessibility for hyperbolic groups
Copyright policy )Strong accessibility for hyperbolic groups
We use an accessibility result of Delzant and Potyagailo to prove Swarup's Strong Accessibility Conjecture for Gromov hyperbolic groups with no 2-torsion. It follows that, if M is an irreducible, orientable, compact 3-manifold with hyperbolic fundamental group, then any hierarchy in which M is decomposed alternately along compressing disks and essential annuli is finite.
18 pages, 6 figures; modified due to an error in v1
- University of Michigan Ann Arbor United States
- Binghamton University United States
Free products of groups, free products with amalgamation, Higman-Neumann-Neumann extensions, and generalizations, Topological methods in group theory, hierarchies, Bass–Serre theory, Group Theory (math.GR), Embeddings and immersions in topological manifolds, finitely generated groups, Hyperbolic groups and nonpositively curved groups, 57M99, Mathematics - Geometric Topology, 57N35, FOS: Mathematics, 20F65, strong accessibility results, 20E08, Bass-Serre theory, free product decompositions, graphs of groups decompositions, 20F67, Geometric Topology (math.GT), hyperbolic groups, families of subgroups, Groups acting on trees, Geometric group theory, group accessibility, Mathematics - Group Theory
Free products of groups, free products with amalgamation, Higman-Neumann-Neumann extensions, and generalizations, Topological methods in group theory, hierarchies, Bass–Serre theory, Group Theory (math.GR), Embeddings and immersions in topological manifolds, finitely generated groups, Hyperbolic groups and nonpositively curved groups, 57M99, Mathematics - Geometric Topology, 57N35, FOS: Mathematics, 20F65, strong accessibility results, 20E08, Bass-Serre theory, free product decompositions, graphs of groups decompositions, 20F67, Geometric Topology (math.GT), hyperbolic groups, families of subgroups, Groups acting on trees, Geometric group theory, group accessibility, Mathematics - Group Theory
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