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Strong accessibility for hyperbolic groups. (English) Zbl 1194.20047
Summary: We use an accessibility result of T. Delzant and L. Potyagailo [Topology 40, No. 3, 617-629 (2001; Zbl 0996.20027)] 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.

20F67 Hyperbolic groups and nonpositively curved groups
20E06 Free products of groups, free products with amalgamation, Higman-Neumann-Neumann extensions, and generalizations
20F65 Geometric group theory
20E08 Groups acting on trees
57M07 Topological methods in group theory
57N35 Embeddings and immersions in topological manifolds
Full Text: DOI arXiv
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