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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.

##### MSC:
 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
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