Algebraic & Geometric Topology 8 (2008) 1459–1479

DOI: 10.2140/agt.2008.8.1459

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

Primary: 20E08, 20F65

Secondary: 20F67, 57M99, 57N35

References

Publication

Received: 17 August 2007
Revised: 12 December 2007
Accepted: 20 February 2008
Published: 5 September 2008

Authors