#### Volume 8, issue 3 (2008)

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Strong accessibility for hyperbolic groups

### Diane M Vavrichek

Algebraic & Geometric Topology 8 (2008) 1459–1479
##### Abstract

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.

##### Keywords
group accessibility, hierarchies, hyperbolic groups, Bass–Serre theory
##### Mathematical Subject Classification 2000
Primary: 20E08, 20F65
Secondary: 57M99, 57N35, 20F67
##### Publication
Received: 17 August 2007
Revised: 12 December 2007
Accepted: 20 February 2008
Published: 5 September 2008
##### Authors
 Diane M Vavrichek Department of Mathematical Sciences Binghamton University Binghamton NY 13902-6000 USA http://www.math.binghamton.edu/vavrichek/