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Strong accessibility for hyperbolic groups
Diane M Vavrichek
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Algebraic & Geometric Topology 8
(2008) 1459–1479
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Abstract
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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.
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Keywords
group accessibility, hierarchies,
hyperbolic groups, Bass–Serre theory
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Mathematical Subject Classification
Primary: 20E08, 20F65
Secondary: 20F67, 57M99, 57N35
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Publication
Received: 17 August 2007
Revised: 12 December 2007
Accepted: 20 February 2008
Published: 5 September 2008
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